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**Review Ch. 10 Complete all problems on a separate sheet of paper.**

Be sure to number each problem. Good Luck!

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**Find the exact length of arc AB, if circle**

Problem #1 Find the exact length of arc AB, if circle P has a radius of 18cm. A P 100° B

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Solution to #1 Arc Length = (100/360) * 36π = (5/18) * 36π = 10π cm.

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Problem # 2 Find the diameter of a circle in which a 36 cm chord is 80 cm from the center.

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

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**Find the radius of a circle with a circumference of**

Problem #3 Find the radius of a circle with a circumference of

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Solution to #3 Circumference = π * diameter so the diameter must be 20 so radius = 10.

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**Find the measure of arc AE.**

Problem #4 Find the measure of arc AE. A 200о B x 210о D E C

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Solution to #4 *Arc BC = 360 – 210 = 150о *Angle BDC is supp (tangent-tangent) = 30о *So Angle ADE = 30о *So 30 = (1/2)(200 – x) 60 = 200 – x x = 140о

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

Problem #5 In the circumscribed polygon, find the length of the AB. 15 A 10 B 12

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Solution to #5 AB = 15 – (10 – x) + 12 – x = 5 + x + 12 – x = 17

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**In circle O, AB is a diameter.**

Problem #6 In circle O, AB is a diameter. OA=3x+5 and OB=2(5x-1). Find AB.

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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

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Problem #7 Solve for x if and if A B C

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Solution to #7 Since angle A is inscribed; 2(5x + 6) = 12x – 2 10x + 12 = 12x – 2 14 = 2x x = 7

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**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

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Solution to #8 Opp. Angles of inscribed quadrilaterals are supp. Measure of Angle T = 180 – 78 = 102о

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

Problem #9 Find the radius of the circle if AB is a diameter, , and BC=20. A B C

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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 *Radius of AB is 20.

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

Problem #10 A circle is inscribed in triangle ABC. AB=14, AC=12 and BC=4. Find BD. A B C D

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Solution to #10 14 – x + 12 – x = 4 26 – 2x = 4 22 = 2x x = 11 So BD = 14 – x = 3

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Problem #11 A circle has a radius of 50. How far from the center is a chord of length 28?

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Solution to #11 7, 24, 25 right triangle So x = 2 * 24 = 48

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**A regular octagon is inscribed in a circle. **

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?

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Solution to #12 * Regular - so all chords congruent. * Congruent chords = congruent arcs. 360/8 = 45о

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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.

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**Solution to #13 3, 4, 5 right triangle x = 12 so length of the chord**

is 24.

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

Problem #14 A 12 by 10 rectangle is inscribed in a circle. Find the radius.

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Solution to #14 = c2 244 = c2

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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

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Solution to #15 Angle P = (1/2)(122 – 68) = (1/2)(54) = 27о

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Problem #16 Find the circumference of a circle in which an 80 cm chord is 9 cm from the center.

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**Solution to #16 9, 40, 41 right triangle so r = 41 C = 2π(41)**

= 82 π cm

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Problem #17 A central angle intercepts an arc that is 5/12 of the circle. Find the measure of angle x. O x of circle O

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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

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**If PA and PB are tangent to circle O at A**

Problem #18 If PA and PB are tangent to circle O at A and B, PA=24, and PO=26, find perimeter of quadrilateral PAOB. A O P B

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**Solution to #18 OA is perpendicular to PA 5, 12, 13 right triangle.**

OA = 10 and PB = 24 = 68

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**Find the measure of angle x.**

Problem #19 Find the measure of angle x. x 44° 92°

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Solution to #19

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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?

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Solution to #20

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Problem #21 Parallelogram ABCD is inscribed in circle Q, with dimensions of 24 by 10. Find the area of circle Q.

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Solution to #21

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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

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Solution to #22

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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°

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Solution to #23

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**Problem #24 AB & AC are tangent to the circle.**

Find the measure of arc BDC. A B C D 76°

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Solution to #24

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STUDY!!!!!

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