Circles

Problem 1

Prove that if $B P$ and $P Q$ are tangents, then (i) $A B \parallel P Q$ and (ii) $M P \times A M = B M \times M Q$ .

See Solution

Problem 2

Prove that in a given diagram, (i) $A B$ is parallel to $P Q$ and (ii) $M P \times A M = B M \times M Q$ .

See Solution

Problem 3

Prove that if $B P$ and $P Q$ are tangents to circles, then (i) $A B \parallel P Q$ and (ii) $M P \times A M = B M \times M Q$ .

See Solution

Problem 4

Find the area of a circular tray with a diameter of 28 cm. Use $\pi=\frac{22}{7}$ .

See Solution

Problem 5

Prove that for a sector with radius $r$ cm and perimeter 50 cm, $\theta = \frac{360}{\pi} \left(\frac{25}{r} - 1\right)$ .

See Solution

Problem 6

Determine the center and radius of the circle given by $(x-2)^{2}+(y+3)^{2}=36$ .

See Solution

Problem 7

Find the parametrization of the circle centered at $1-i$ with radius 3: $z(t)=$ .

See Solution

Problem 8

Find the tangent line equation at $(0,2)$ for the circle $(x+2)^{2}+(y+1)^{2}=13$ .

See Solution

Problem 9

Find the equation of the circle with endpoints of the diameter at P=(-3,-2) and Q=(1,6). $(x-[?])^{2}+(y-[])^{2} =$

See Solution

Problem 10

Find the center and radius of the circle: $(x+9)^{2}+(y-6)^{2}=25$ . Center = ([?], []), Radius = [].

See Solution

Problem 11

Find the radius of a circle with a circumference of $56 \mathrm{~mm}$ .

See Solution

Problem 12

Prove that in cyclic quadrilateral $ABCD$ , the lines $XY$ and $ZW$ are parallel, where $X$ , $Y$ , $Z$ , and $W$ are feet of perpendiculars.

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Problem 13

Four points A, B, C, D on a semicircle satisfy $|\overrightarrow{\mathrm{AB}}|=|\overrightarrow{\mathrm{BC}}|=|\overrightarrow{\mathrm{CD}}|$ . Assess the validity of assertions A and R.

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Problem 14

Find the Earth's orbital speed given a radius of 1.49 x $10^8$ km and a period of 5.25 days.

See Solution

Problem 15

Find the radius of a circle with circumference equal to the sum of two circles with radii $19 \mathrm{~cm}$ and $9 \mathrm{~cm}$ .

See Solution

Problem 16

Find the length of TA where $OT = 4 \mathrm{~cm}$ and $\angle OTA = 30^{\circ}$ . Choices: (a) $2\sqrt{3} \mathrm{~cm}$ (b) $2 \mathrm{~cm}$ (c) $2\sqrt{2} \mathrm{~cm}$ (d) $\sqrt{3} \mathrm{~cm}$ .

See Solution

Problem 17

Calculate the shaded area of a quarter circle with radius $r = 12$ units.

See Solution

Problem 18

Find the refractive index $\mu$ of a sphere with radius $R$ and a cavity of radius $R/2$ focusing light at point P. Options: (a) $\mu=\frac{3+\sqrt{5}}{2}$ , (b) $\mu=\frac{3-\sqrt{5}}{2}$ , (c) $\mu=3+\sqrt{5}$ , (d) $\mu=\frac{1+\sqrt{5}}{2}$ .

See Solution

Problem 19

Find the length of arc $F \widehat{G H}$ in a circle with radius $50 \mathrm{~cm}$ and central angle $98^{\circ}$ .

See Solution

Problem 20

Find the area of a shaded sector in a circle with radius 16 units and central angle $60^{\circ}$ .

See Solution

Problem 21

Determine the general equation of the circle from $(x-2)^{2}+(y+1)^{2}=10$ . Show all steps.

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Problem 22

Find the radius $r$ and angle $\theta$ of a sector with area $10 \mathrm{~cm}^{2}$ and perimeter $13 \mathrm{~cm}$ .

See Solution

Problem 23

Find the angle and arc length of a sector with radius 25 cm, where the sector's area is $1/5$ of the circle's area.

See Solution

Problem 24

Determine the general equation of the circle given by $\left(x-\frac{3}{2}\right)^{2}+\left(y+\frac{5}{2}\right)^{2}=14$ .

See Solution

Problem 25

Find the center and radius of the circle defined by the equation $(x-\frac{3}{2})^{2}+(y+\frac{5}{2})^{2}=14$ .

See Solution

Problem 26

Determine the standard equation of the circle from $x^{2}+y^{2}-400=0$ .

See Solution

Problem 27

Determine the equation, center, and radius of the circle defined by $x^{2}+y^{2}=169$ .

See Solution

Problem 28

Find the general equation, center, and radius of the circle given by $x^{2} + y^{2} = 16$ .

See Solution

Problem 29

Find the equations of a circle centered at $(0,0)$ with radius $3$ , given a point $(0,4)$ on it.

See Solution

Problem 30

Determine the circle's equation, center, and radius from $(x+3)^{2}+y^{2}=25$ .

See Solution

Problem 31

Determine the general equation of the circle from $x^{2}+y^{2}=169$ .

See Solution

Problem 32

Solve the equation $x^{2}+y^{2}-10y+21=0$ for $y$ .

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Problem 33

Convert $x^{2}+y^{2}-10x+6y+22=0$ to circle form $(x-h)^2 + (y-k)^2 = r^2$ ; find center `(h,k)` and radius `r`.

See Solution

Problem 34

Find the circle's equations with center $(-5,-3)$ and radius 4: standard and general forms.

See Solution

Problem 35

Find the center $(h, k)$ and radius $r$ of the circle from $(x-h)^{2}+(y-k)^{2}=r^{2}$ . Derive the general equation of a circle.

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Problem 36

Find the distance from the point $(-1, -3)$ to the circle defined by $x^{2}+y^{2}+2x+6y-6=0$ ; it's 4 units.

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Problem 37

Convert the circle equation $x^{2}+y^{2}+x-3y-\frac{1}{2}=0$ to standard form and find its center and radius.

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Problem 38

Find the area of a circle with a radius of 10 inches using $A=\pi r^{2}$ and $\pi=3.14$ . Choices: A) $3.14 \mathrm{in}^{2}$ B) $31.4 \mathrm{in}^{2}$ C) $314 \mathrm{in}^{2}$ D) $3,140 \mathrm{in}^{2}$ E) $31,400 \mathrm{in}^{2}$

See Solution

Problem 39

Berechne den Umfang und Flächeninhalt eines runden Tisches mit $r=25 \mathrm{~cm}$ .

See Solution

Problem 40

Determine the general equation of the circle defined by $x^{2}+y^{2}=16$ .

See Solution

Problem 41

Find the total length of two semicircles with centers $R$ and $S$ , where $RS=12$ . Options are: (A) $8 \pi$ , (B) $9 \pi$ , (C) $12 \pi$ , (D) $15 \pi$ , (E) $16 \pi$ .

See Solution

Problem 42

Sebuah papan sasar bulatan dengan jejari $20 \mathrm{~cm}$ . Beza jejari antara bulatan $P, Q, R, S$ dan $T$ ialah $4 \mathrm{~cm}$ .
Hitung: (a) Beza lilitan bulatan $T$ dan $P$ . (b) Luas kawasan $P$ dan $R$ (gunakan $\pi=\frac{22}{7}$ ).

See Solution

Problem 43

Hitung (a) beza lilitan bulatan $T$ dan $P$ dalam $\mathrm{cm}$ , (b) luas kawasan $P$ dan $R$ dalam $\mathrm{cm}^{2}$ . Gunakan $\left.\pi=\frac{22}{7}\right.$

See Solution

Problem 44

Hitung beza lilitan bulatan $T$ dan $P$ , serta luas kawasan $P$ dan $R$ dengan $\pi=\frac{22}{7}$ .

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Problem 45

A circle sector with radius 5 cm and angle 144° forms a cone. Find: 1) base radius, 2) height, 3) volume, 4) surface area, 5) vertical angle.

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Problem 46

A disc of radius $30 \mathrm{~cm}$ has supports $20 \mathrm{~cm}$ tall. Find: (a) $\angle A O B$ , (b) arc length $A C B$ , (c) area percentage above line $A B$ .

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Problem 47

1. Earth’s radius is $6371 \mathrm{~km}$ . Distance Dhaka to Delhi is $1882 \mathrm{~km}$ . Find the angle at Earth's center.
2. Cyclist travels from A to B at 250 m/min, with an angle of $1^{\circ} 5^{\prime}$ at Earth's center ( $6440 \mathrm{~km}$ radius). Time taken in hours?
3. Circle radius is 35 m. An arc subtends angle $\frac{\pi}{4}$ at the center. Find the arc length.

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Problem 48

Find the length of an arc with a radius of 35 m and subtending an angle of $\frac{\pi}{4}$ at the center.

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Problem 49

Calculate the arc length for a circle with radius 35 m and angle $\frac{\pi}{4}$ radians.

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Problem 50

A clock's minute hand is $12 \mathrm{~cm}$ long. What distance does it cover in 15 minutes?

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Problem 51

Find the radius of a circle with a circumference of 25.12 miles using the formula $C = 2\pi r$ .

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Problem 52

Find the area of a circle with a radius of 4 km using $\pi \approx 3.14$ .

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Problem 53

Find the radius of a circle with an area of 78.5 sq ft, using $\pi \approx 3.14$ .

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Problem 54

Find the diameter of a circle with a circumference of 41.448 inches. Use $\pi \approx 3.14$ .

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Problem 55

Find the area of a circle with a diameter of 2 cm. Use $\pi \approx 3.14$ .

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Problem 56

Find the circumference of a circle with an area of 50.24 sq. yards, using $\pi \approx 3.14$ .

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Problem 57

Find the area of a circle with a circumference of 14.444 inches. Use $\pi \approx 3.14$ and round to the nearest hundredth.

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Problem 58

Find the circumference of a circle with an area of 12.56 in², using $\pi \approx 3.14$ .

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Problem 59

Find the area of a circle with a circumference of 12.56 yards, using $\pi \approx 3.14$ .

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Problem 60

Find the area of a campaign button with a diameter of 4 inches using $\pi \approx 3.14$ . Round to the nearest hundredth.

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Problem 61

A circular stained-glass window has a circumference of 6.28 yards. What is its diameter? Use $\pi \approx 3.14$ .

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Problem 62

Find the circumference of a circle with area 0.2826 mm² using $\pi \approx 3.14$ ; round to the nearest hundredth.

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Problem 63

Find the diameter of a merry-go-round with an area of 78.5 sq ft. Use $\pi \approx 3.14$ and round to the nearest hundredth.

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Problem 64

Miranda's trampoline has a circumference of 12.56 m. What is the radius? Use $\pi \approx 3.14$ and round to the nearest hundredth.

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Problem 65

A coffee mug has a diameter of 4 inches. Find the circumference using $\pi \approx 3.14$ . Round to the nearest hundredth.

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Problem 66

Find the circumference of a coffee mug with a diameter of 4 inches using $\pi \approx 3.14$ . Round to the nearest hundredth.

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Problem 67

Find the area of a circular searchlight with a radius of 2 feet using $\pi \approx 3.14$ . Round to the nearest hundredth.

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Problem 68

A jailer has a key ring with a circumference of 10.676 inches. Find its radius using $\pi \approx 3.14$ . Round to the nearest hundredth.

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Problem 69

A button has an area of 50.24 mm². What is its circumference using $\pi \approx 3.14$ ? Round to the nearest hundredth.

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Problem 70

Find the area of a circular rug with a circumference of 10.048 yards. Use $\pi \approx 3.14$ and round to the nearest hundredth.

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Problem 71

Find the circumference of a telescope lens with an area of 3.7994 square yards. Use $\pi \approx 3.14$ and round to the nearest hundredth.

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Problem 72

A merry-go-round's circular platform has an area of 3.14 sq. yards. Find its circumference using $\pi \approx 3.14$ . Round to the nearest hundredth.

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Problem 73

Wesley has a round tablecloth with a radius of 1.2 yards. Find its circumference using $\pi \approx 3.14$ . Round to the nearest hundredth.

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Problem 74

Find the area of a semicircle with a radius of 1 yard. Use the formula: Area = $\frac{1}{2} \pi r^2$ .

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Problem 75

An anthropologist finds an igloo with a circumference of 14.444 yards. What is the area of the floor? Use $\pi \approx 3.14$ . Round to the nearest hundredth. square yards

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Problem 76

Find the area of a quarter circle with a radius of 3 miles. Use the formula $A = \frac{1}{4} \pi r^2$ .

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Problem 77

Find the area of a semicircle with a radius of 4 mm. Use the formula: Area = $\frac{1}{2} \pi r^2$ .

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Problem 78

Find the area of a semicircle with a diameter of 6 feet. Use the formula $A = \frac{1}{2} \pi r^2$ .

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Problem 79

Find the radius and perimeter of sector $OAB$ with area $24\pi \mathrm{cm}^2$ and angle $60^\circ$ . Also, find the area of the circle with $AB$ as diameter.

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Problem 80

In sectors $O A B$ and $O C D$ , with $O A=27 \mathrm{~cm}$ , $O C=15 \mathrm{~cm}$ , and shaded area $147 \pi \mathrm{cm}^{2}$ , find: (a) $\angle A O B$ ; (b) perimeter of shaded region in terms of $\pi$ .

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Problem 81

Help Milynn find the center of the next circle for her inscribed triangle. Consider previous circles, rules, and vertex positions.

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Problem 82

A spiral is made of semicircles with the first diameter $10 \mathrm{~cm}$ , each next being $\frac{4}{5}$ of the last.
1) Find the total length of the spiral.
2) How far is point $E$ (midpoint of the 6th semicircle) from point $A$ ?

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Problem 83

What is the circumference of a circle drawn with a 10-inch chain? Use $\pi \approx 3.14$ . Options: (A) 15.70 (B) 23.14 (C) 31.40 (D) 62.80.

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Problem 84

Find the central angle in radians and degrees for an arc length of 10 inches on a circle with radius 4 inches.

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Problem 85

Find the total time to walk around a circle if it takes 9 minutes to walk from house 1 to house 4.

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Problem 86

If 12 houses are spaced equally in a circle and walking from house 1 to house 4 takes 9 minutes, how long for a full circle?

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Problem 87

45 and 50 are spaced around a circle. If it takes 9 min to walk from house 1 to house 4, how long for a full circle?

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Problem 88

The sum of the squares of $x$ and $y$ equals 8: $x^{2}+y^{2}=8$ .

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Problem 89

Is it true that if two chords in the same circle are congruent, their minor areas are also congruent? A. Yes B. No C. Maybe D. Sometimes E. Not applicable

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Problem 90

Find the perimeter of a square inscribed in a circle with area $50 \pi$ . Options: A. 5 B. 10 C. 20 D. 40 E. 50

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Problem 91

Find the perimeter of a square inscribed in a circle with area $50 \pi$ .

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Problem 92

A square with area 36 is inscribed in a circle. Find the circle's circumference. A. $3 \pi$ B. $(3 \sqrt{2}) \pi$ C. $6 \pi$ D. $(6 \sqrt{2}) \pi$ E. $36 \pi$

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Problem 93

Find the circumference of a parachute with a radius of 16 feet. Choose the closest option: A. $100.48 \mathrm{ft}$ B. $198.4 \mathrm{ft}$ C. $49.6 \mathrm{ft}$ D. $803.84 \mathrm{ft}$ .

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Problem 94

Find the area of a circular sign with an 18-inch diameter. Choices: A) $56.52 \mathrm{in}^{2}$ B) $101.36 \mathrm{in}^{2}$ C) $188.78 \mathrm{in}^{2}$ D) $254.34 \mathrm{in}^{2}$ .

See Solution

Problem 95

Find the radius of the circle given by the equation $(x-9)^{2}+(y-3)^{2}=64$ .

See Solution

Problem 96

Circle A's equation is $(x-3)^{2}+(y+1)^{2}=16$ . What is the equation of circle B after translating A right by 2 units?

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Problem 97

Find the area of a circle with radius 13 m. Options: A. $4 m^{2}$ B. $8 m^{2}$ C. $6.28 m^{2}$ D. $12.57 m^{2}$
Calculate the volume of a sphere with radius 13 m. Options: A. $14,356.32 m^{3}$ B. $427.74 m^{3}$ C. $141.58 m^{3}$ D. $161,747.92 m^{3}$
What is the radius of a sphere with surface area $616 cm^{2}$ ? Options: A. $7 cm$ B. $14 cm$ C. $21 cm$ D. $28 cm$
Find the slant height of a cone formed by rolling a semi-circle of radius $10 cm$ . Options: A. $5 cm$ B. $10 cm$ C. $15 cm$

See Solution

Problem 98

Find the area of a circular rug with a radius of 4 feet in square inches. Choices: A. $55.26 \mathrm{ft}^{2}$ B. $50.24 \mathrm{ft}^{2}$ C. $29.7 \mathrm{ft}^{2}$ D. $33.6 \mathrm{ft}^{2}$

See Solution

Problem 99

Find the area of a circle with a diameter of $6 \mathrm{ft}$ . Choices: a. 37.7 b. 3.14 C. 28.27 d. 113.1

See Solution

Problem 100

Calculate the circumference and area of a circle with diameter $6 \mathrm{yd}$ using $\pi \approx 3.14$ . Include units.

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Circles

Problem 1

Prove that if BP B P BP and PQ P Q PQ are tangents, then (i) AB∥PQ A B \parallel P Q AB∥PQ and (ii) MP×AM=BM×MQ M P \times A M = B M \times M Q MP×AM=BM×MQ.

Problem 2

Prove that in a given diagram, (i) AB A B AB is parallel to PQ P Q PQ and (ii) MP×AM=BM×MQ M P \times A M = B M \times M Q MP×AM=BM×MQ.

Problem 3

Prove that if BP B P BP and PQ P Q PQ are tangents to circles, then (i) AB∥PQ A B \parallel P Q AB∥PQ and (ii) MP×AM=BM×MQ M P \times A M = B M \times M Q MP×AM=BM×MQ.

Problem 4

Find the area of a circular tray with a diameter of 28 cm. Use π=227\pi=\frac{22}{7}π=722​.

Problem 5

Prove that for a sector with radius rrr cm and perimeter 50 cm, θ=360π(25r−1)\theta = \frac{360}{\pi} \left(\frac{25}{r} - 1\right)θ=π360​(r25​−1).

Problem 6

Determine the center and radius of the circle given by (x−2)2+(y+3)2=36(x-2)^{2}+(y+3)^{2}=36(x−2)2+(y+3)2=36.

Problem 7

Find the parametrization of the circle centered at 1−i1-i1−i with radius 3: z(t)=z(t)=z(t)=.

Problem 8

Find the tangent line equation at (0,2)(0,2)(0,2) for the circle (x+2)2+(y+1)2=13(x+2)^{2}+(y+1)^{2}=13(x+2)2+(y+1)2=13.

Problem 9

Find the equation of the circle with endpoints of the diameter at P=(-3,-2) and Q=(1,6). (x−[?])2+(y−[])2= (x-[?])^{2}+(y-[])^{2} = (x−[?])2+(y−[])2=

Problem 10

Find the center and radius of the circle: (x+9)2+(y−6)2=25(x+9)^{2}+(y-6)^{2}=25(x+9)2+(y−6)2=25. Center = ([?], []), Radius = [].

Problem 11

Find the radius of a circle with a circumference of 56 mm56 \mathrm{~mm}56 mm.

Problem 12

Prove that in cyclic quadrilateral ABCDABCDABCD, the lines XYXYXY and ZWZWZW are parallel, where XXX, YYY, ZZZ, and WWW are feet of perpendiculars.

Problem 13

Four points A, B, C, D on a semicircle satisfy ∣ABundefined∣=∣BCundefined∣=∣CDundefined∣|\overrightarrow{\mathrm{AB}}|=|\overrightarrow{\mathrm{BC}}|=|\overrightarrow{\mathrm{CD}}|∣AB∣=∣BC∣=∣CD∣. Assess the validity of assertions A and R.

Problem 14

Find the Earth's orbital speed given a radius of 1.49 x 10810^8108 km and a period of 5.25 days.

Problem 15

Find the radius of a circle with circumference equal to the sum of two circles with radii 19 cm19 \mathrm{~cm}19 cm and 9 cm9 \mathrm{~cm}9 cm.

Problem 16

Find the length of TA where OT=4 cmOT = 4 \mathrm{~cm}OT=4 cm and ∠OTA=30∘\angle OTA = 30^{\circ}∠OTA=30∘. Choices: (a) 23 cm2\sqrt{3} \mathrm{~cm}23​ cm (b) 2 cm2 \mathrm{~cm}2 cm (c) 22 cm2\sqrt{2} \mathrm{~cm}22​ cm (d) 3 cm\sqrt{3} \mathrm{~cm}3​ cm.

Problem 17

Calculate the shaded area of a quarter circle with radius r=12r = 12r=12 units.

Problem 18

Problem 19

Find the length of arc FGHundefinedF \widehat{G H}FGH in a circle with radius 50 cm50 \mathrm{~cm}50 cm and central angle 98∘98^{\circ}98∘.

Problem 20

Find the area of a shaded sector in a circle with radius 16 units and central angle 60∘60^{\circ}60∘.

Problem 21

Determine the general equation of the circle from (x−2)2+(y+1)2=10(x-2)^{2}+(y+1)^{2}=10(x−2)2+(y+1)2=10. Show all steps.

Problem 22

Find the radius rrr and angle θ\thetaθ of a sector with area 10 cm210 \mathrm{~cm}^{2}10 cm2 and perimeter 13 cm13 \mathrm{~cm}13 cm.

Problem 23

Find the angle and arc length of a sector with radius 25 cm, where the sector's area is 1/51/51/5 of the circle's area.

Problem 24

Determine the general equation of the circle given by (x−32)2+(y+52)2=14\left(x-\frac{3}{2}\right)^{2}+\left(y+\frac{5}{2}\right)^{2}=14(x−23​)2+(y+25​)2=14.

Problem 25

Find the center and radius of the circle defined by the equation (x−32)2+(y+52)2=14(x-\frac{3}{2})^{2}+(y+\frac{5}{2})^{2}=14(x−23​)2+(y+25​)2=14.

Problem 26

Determine the standard equation of the circle from x2+y2−400=0x^{2}+y^{2}-400=0x2+y2−400=0.

Problem 27

Determine the equation, center, and radius of the circle defined by x2+y2=169x^{2}+y^{2}=169x2+y2=169.

Problem 28

Find the general equation, center, and radius of the circle given by x2+y2=16x^{2} + y^{2} = 16x2+y2=16.

Problem 29

Find the equations of a circle centered at (0,0)(0,0)(0,0) with radius 333, given a point (0,4)(0,4)(0,4) on it.

Problem 30

Determine the circle's equation, center, and radius from (x+3)2+y2=25(x+3)^{2}+y^{2}=25(x+3)2+y2=25.

Problem 31

Determine the general equation of the circle from x2+y2=169x^{2}+y^{2}=169x2+y2=169.

Problem 32

Solve the equation x2+y2−10y+21=0x^{2}+y^{2}-10y+21=0x2+y2−10y+21=0 for yyy.

Problem 33

Convert x2+y2−10x+6y+22=0x^{2}+y^{2}-10x+6y+22=0x2+y2−10x+6y+22=0 to circle form (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2(x−h)2+(y−k)2=r2; find center `(h,k)` and radius `r`.

Problem 34

Find the circle's equations with center (−5,−3)(-5,-3)(−5,−3) and radius 4: standard and general forms.

Problem 35

Find the center (h,k)(h, k)(h,k) and radius rrr of the circle from (x−h)2+(y−k)2=r2(x-h)^{2}+(y-k)^{2}=r^{2}(x−h)2+(y−k)2=r2. Derive the general equation of a circle.

Problem 36

Find the distance from the point (−1,−3)(-1, -3)(−1,−3) to the circle defined by x2+y2+2x+6y−6=0x^{2}+y^{2}+2x+6y-6=0x2+y2+2x+6y−6=0; it's 4 units.

Problem 37

Convert the circle equation x2+y2+x−3y−12=0x^{2}+y^{2}+x-3y-\frac{1}{2}=0x2+y2+x−3y−21​=0 to standard form and find its center and radius.

Problem 38

Problem 39

Berechne den Umfang und Flächeninhalt eines runden Tisches mit r=25 cmr=25 \mathrm{~cm}r=25 cm.

Problem 40

Determine the general equation of the circle defined by x2+y2=16x^{2}+y^{2}=16x2+y2=16.

Problem 41

Prove that if $B P$ and $P Q$ are tangents, then (i) $A B \parallel P Q$ and (ii) $M P \times A M = B M \times M Q$ .

Prove that in a given diagram, (i) $A B$ is parallel to $P Q$ and (ii) $M P \times A M = B M \times M Q$ .

Prove that if $B P$ and $P Q$ are tangents to circles, then (i) $A B \parallel P Q$ and (ii) $M P \times A M = B M \times M Q$ .

Find the area of a circular tray with a diameter of 28 cm. Use $\pi=\frac{22}{7}$ .

Prove that for a sector with radius $r$ cm and perimeter 50 cm, $\theta = \frac{360}{\pi} \left(\frac{25}{r} - 1\right)$ .

Determine the center and radius of the circle given by $(x-2)^{2}+(y+3)^{2}=36$ .

Find the parametrization of the circle centered at $1-i$ with radius 3: $z(t)=$ .

Find the tangent line equation at $(0,2)$ for the circle $(x+2)^{2}+(y+1)^{2}=13$ .

Find the equation of the circle with endpoints of the diameter at P=(-3,-2) and Q=(1,6). $(x-[?])^{2}+(y-[])^{2} =$

Find the center and radius of the circle: $(x+9)^{2}+(y-6)^{2}=25$ . Center = ([?], []), Radius = [].

Find the radius of a circle with a circumference of $56 \mathrm{~mm}$ .

Prove that in cyclic quadrilateral $ABCD$ , the lines $XY$ and $ZW$ are parallel, where $X$ , $Y$ , $Z$ , and $W$ are feet of perpendiculars.

Four points A, B, C, D on a semicircle satisfy $|\overrightarrow{\mathrm{AB}}|=|\overrightarrow{\mathrm{BC}}|=|\overrightarrow{\mathrm{CD}}|$ . Assess the validity of assertions A and R.

Find the Earth's orbital speed given a radius of 1.49 x $10^8$ km and a period of 5.25 days.

Find the radius of a circle with circumference equal to the sum of two circles with radii $19 \mathrm{~cm}$ and $9 \mathrm{~cm}$ .

Find the length of TA where $OT = 4 \mathrm{~cm}$ and $\angle OTA = 30^{\circ}$ . Choices: (a) $2\sqrt{3} \mathrm{~cm}$ (b) $2 \mathrm{~cm}$ (c) $2\sqrt{2} \mathrm{~cm}$ (d) $\sqrt{3} \mathrm{~cm}$ .

Calculate the shaded area of a quarter circle with radius $r = 12$ units.

Find the length of arc $F \widehat{G H}$ in a circle with radius $50 \mathrm{~cm}$ and central angle $98^{\circ}$ .

Find the area of a shaded sector in a circle with radius 16 units and central angle $60^{\circ}$ .

Determine the general equation of the circle from $(x-2)^{2}+(y+1)^{2}=10$ . Show all steps.

Find the radius $r$ and angle $\theta$ of a sector with area $10 \mathrm{~cm}^{2}$ and perimeter $13 \mathrm{~cm}$ .

Find the angle and arc length of a sector with radius 25 cm, where the sector's area is $1/5$ of the circle's area.

Determine the general equation of the circle given by $\left(x-\frac{3}{2}\right)^{2}+\left(y+\frac{5}{2}\right)^{2}=14$ .

Find the center and radius of the circle defined by the equation $(x-\frac{3}{2})^{2}+(y+\frac{5}{2})^{2}=14$ .

Determine the standard equation of the circle from $x^{2}+y^{2}-400=0$ .

Determine the equation, center, and radius of the circle defined by $x^{2}+y^{2}=169$ .

Find the general equation, center, and radius of the circle given by $x^{2} + y^{2} = 16$ .

Find the equations of a circle centered at $(0,0)$ with radius $3$ , given a point $(0,4)$ on it.

Determine the circle's equation, center, and radius from $(x+3)^{2}+y^{2}=25$ .

Determine the general equation of the circle from $x^{2}+y^{2}=169$ .

Solve the equation $x^{2}+y^{2}-10y+21=0$ for $y$ .

Convert $x^{2}+y^{2}-10x+6y+22=0$ to circle form $(x-h)^2 + (y-k)^2 = r^2$ ; find center `(h,k)` and radius `r`.

Find the circle's equations with center $(-5,-3)$ and radius 4: standard and general forms.

Find the center $(h, k)$ and radius $r$ of the circle from $(x-h)^{2}+(y-k)^{2}=r^{2}$ . Derive the general equation of a circle.

Find the distance from the point $(-1, -3)$ to the circle defined by $x^{2}+y^{2}+2x+6y-6=0$ ; it's 4 units.

Convert the circle equation $x^{2}+y^{2}+x-3y-\frac{1}{2}=0$ to standard form and find its center and radius.

Berechne den Umfang und Flächeninhalt eines runden Tisches mit $r=25 \mathrm{~cm}$ .

Determine the general equation of the circle defined by $x^{2}+y^{2}=16$ .

Find the total length of two semicircles with centers $R$ and $S$ , where $RS=12$ . Options are: (A) $8 \pi$ , (B) $9 \pi$ , (C) $12 \pi$ , (D) $15 \pi$ , (E) $16 \pi$ .

Sebuah papan sasar bulatan dengan jejari $20 \mathrm{~cm}$ . Beza jejari antara bulatan $P, Q, R, S$ dan $T$ ialah $4 \mathrm{~cm}$ .
Hitung: (a) Beza lilitan bulatan $T$ dan $P$ . (b) Luas kawasan $P$ dan $R$ (gunakan $\pi=\frac{22}{7}$ ).

Hitung (a) beza lilitan bulatan $T$ dan $P$ dalam $\mathrm{cm}$ , (b) luas kawasan $P$ dan $R$ dalam $\mathrm{cm}^{2}$ . Gunakan $\left.\pi=\frac{22}{7}\right.$

Hitung beza lilitan bulatan $T$ dan $P$ , serta luas kawasan $P$ dan $R$ dengan $\pi=\frac{22}{7}$ .

A disc of radius $30 \mathrm{~cm}$ has supports $20 \mathrm{~cm}$ tall. Find: (a) $\angle A O B$ , (b) arc length $A C B$ , (c) area percentage above line $A B$ .

Find the length of an arc with a radius of 35 m and subtending an angle of $\frac{\pi}{4}$ at the center.

Calculate the arc length for a circle with radius 35 m and angle $\frac{\pi}{4}$ radians.

A clock's minute hand is $12 \mathrm{~cm}$ long. What distance does it cover in 15 minutes?

Find the radius of a circle with a circumference of 25.12 miles using the formula $C = 2\pi r$ .

Find the area of a circle with a radius of 4 km using $\pi \approx 3.14$ .

Find the radius of a circle with an area of 78.5 sq ft, using $\pi \approx 3.14$ .

Find the diameter of a circle with a circumference of 41.448 inches. Use $\pi \approx 3.14$ .

Find the area of a circle with a diameter of 2 cm. Use $\pi \approx 3.14$ .

Find the circumference of a circle with an area of 50.24 sq. yards, using $\pi \approx 3.14$ .

Find the area of a circle with a circumference of 14.444 inches. Use $\pi \approx 3.14$ and round to the nearest hundredth.

Find the circumference of a circle with an area of 12.56 in², using $\pi \approx 3.14$ .

Find the area of a circle with a circumference of 12.56 yards, using $\pi \approx 3.14$ .

Find the area of a campaign button with a diameter of 4 inches using $\pi \approx 3.14$ . Round to the nearest hundredth.

A circular stained-glass window has a circumference of 6.28 yards. What is its diameter? Use $\pi \approx 3.14$ .

Find the circumference of a circle with area 0.2826 mm² using $\pi \approx 3.14$ ; round to the nearest hundredth.

Find the diameter of a merry-go-round with an area of 78.5 sq ft. Use $\pi \approx 3.14$ and round to the nearest hundredth.

Miranda's trampoline has a circumference of 12.56 m. What is the radius? Use $\pi \approx 3.14$ and round to the nearest hundredth.

A coffee mug has a diameter of 4 inches. Find the circumference using $\pi \approx 3.14$ . Round to the nearest hundredth.

Find the circumference of a coffee mug with a diameter of 4 inches using $\pi \approx 3.14$ . Round to the nearest hundredth.

Find the area of a circular searchlight with a radius of 2 feet using $\pi \approx 3.14$ . Round to the nearest hundredth.

A jailer has a key ring with a circumference of 10.676 inches. Find its radius using $\pi \approx 3.14$ . Round to the nearest hundredth.

A button has an area of 50.24 mm². What is its circumference using $\pi \approx 3.14$ ? Round to the nearest hundredth.

Find the area of a circular rug with a circumference of 10.048 yards. Use $\pi \approx 3.14$ and round to the nearest hundredth.

Find the circumference of a telescope lens with an area of 3.7994 square yards. Use $\pi \approx 3.14$ and round to the nearest hundredth.

A merry-go-round's circular platform has an area of 3.14 sq. yards. Find its circumference using $\pi \approx 3.14$ . Round to the nearest hundredth.

Wesley has a round tablecloth with a radius of 1.2 yards. Find its circumference using $\pi \approx 3.14$ . Round to the nearest hundredth.

Find the area of a semicircle with a radius of 1 yard. Use the formula: Area = $\frac{1}{2} \pi r^2$ .