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Review Ch. 10. Complete all problems on a separate sheet of paper. Be sure to number each problem. Good Luck!. Problem #1. Find the exact length of arc AB, if circle P has a radius of 18cm. A. P. 100 °. B. Solution to #1. Arc Length = (100/360) * 36 π

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Review Ch. 10

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Review Ch. 10

Complete all problems on a separate sheet of paper.

Be sure to number each problem. Good Luck!

Problem #1

Find the exactlength of arc AB, if circle

P has a radius of 18cm.

A

P

100°

B

Solution to #1

Arc Length = (100/360) * 36π

= (5/18) * 36π

= 10π cm.

Problem # 2

Find the diameter of a circle in which a 36 cm chord is 80 cm from the center.

Solution to #2

This is a 9, 40, 41 triangle times 2 so r = 82cm  diameter = 164 cm.

Problem #3

Find the radius of a circle with a circumference of

Solution to #3

Circumference = π * diameter  so the

diameter must be 20  so radius = 10.

Problem #4

Find the measure of arc AE.

A

200о

B

x

210о

D

E

C

Solution to #4

*Arc BC = 360 – 210 = 150о

*Angle BDC is supp (tangent-tangent) = 30о

*So 30 = (1/2)(200 – x)

60 = 200 – x

x = 140о

Problem #5

In the circumscribed polygon, find the length of the AB.

15

A

10

B

12

Solution to #5

AB = 15 – (10 – x) + 12 – x

= 5 + x + 12 – x

= 17

Problem #6

In circle O, AB is a diameter.

OA=3x+5 and OB=2(5x-1).

Find AB.

Solution to #6

OA and OB are both radii so are equal.

3x + 5 = 2(5x – 1)

3x + 5 = 10x – 2

7 = 7x

1 = x

each radius = 8 ; so diameter AB = 16

B

C

A

Solve for x if

and if

Solution to #7

Since angle A is inscribed;

2(5x + 6) = 12x – 2

10x + 12 = 12x – 2

14 = 2x

x = 7

Problem #8

MATH is inscribed in the circle.

Angle M has a measure of 78 degrees.

Find the measure of angle T.

A

M

T

H

Solution to #8

Opp. Angles of inscribed quadrilaterals are

supp.

Measure of Angle T = 180 – 78 = 102о

B

C

A

Problem #9

Find the radius of the circle if AB is a diameter, , and BC=20.

Solution to #9

*Measure of Angle B = 120/2 = 60

*Measure of Angle C = 90

*30 – 60 – 90 triangle with x = 20 ; so

diameter is 2x = 40

Problem #10

A circle is inscribed in triangle ABC. AB=14, AC=12 and BC=4. Find BD.

A

B

C

D

Solution to #10

14 – x + 12 – x = 4

26 – 2x = 4

22 = 2x

x = 11

So BD = 14 – x = 3

Problem #11

A circle has a radius of 50. How far from the center is a chord of length 28?

Solution to #11

7, 24, 25 right triangle

So x = 2 * 24 = 48

Problem #12

A regular octagon is inscribed in a circle.

What is the measure of an arc cut off by a side of the octagon?

Solution to #12

* Regular - so all chords congruent.

* Congruent chords = congruent

arcs.

360/8 = 45о

Problem #13

Two concentric circles have radii of lengths 16 and 20. Find the length of a chord of the larger circle that is tangent to the smaller circle.

Solution to #13

• 3, 4, 5 right triangle

x = 12 so length of the chord

is 24.

Problem #14

A 12 by 10 rectangle is inscribed in a circle. Find the radius.

Solution to #14

• 144 + 100 = c2

244 = c2

Problem #15

Two secants drawn to a circle from an external point intercept arcs that are 122° and 68°. Find the measure of the secant-secant angle.

122°

68°

P

Solution to #15

• Angle P = (1/2)(122 – 68)

= (1/2)(54)

= 27о

Problem #16

• Find the circumference of a circle in which an 80 cm chord is 9 cm from the center.

Solution to #16

• 9, 40, 41 right triangle so r = 41

• C = 2π(41)

= 82 π cm

Problem #17

A central angle intercepts an arc that is 5/12 of the circle. Find the measure of angle x.

x

O

of circle O

Solution to #17

• If arc is 5/12  central angle is 5/12 of 360 so central angle is 150о

• Radii are congruent so isosceles triangle  only 30о left.

• Angle x = 30/2 = 15о

Problem #18

If PA and PB are tangent to circle O at A

and B, PA=24, and PO=26, find

A

O

P

B

Solution to #18

• OA is perpendicular to PA  5, 12, 13 right triangle.

• OA = 10 and PB = 24

• 10 + 10 + 24 + 24 = 68

Problem #19

Find the measure of angle x.

x

44°

92°

Problem #20

What is the length of a chord that cuts off an arc of 120 degrees in a circle with a radius of 8?

Problem #21

Parallelogram ABCD is inscribed in circle Q, with dimensions of 24 by 10. Find the area of circle Q.

Problem #22

Circle A has a radius of 5 inches, and circle B has a radius of 20 inches. The centers are 39 inches apart. Find the length of the common external tangent (CD).

D

C

A

B

Problem #23

Two tangent segments of a circle with a diameter of 50 inches form a 60 degree angle where they meet at P. How far is P from the center of the circle?

P

60°

B

D

76°

A

C

Problem #24

AB & AC are tangent to the circle.

Find the measure of arc BDC.