Review Ch. 10
Complete all problems on a separate sheet of paper. Be sure to number each problem. Good Luck!
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
Solution to #5
AB = 15 – (10 – x) + 12 – x
= 5 + x + 12 – x
= 17
B
A
12 - x
12 - x
15 - (10 - x)
15 - (10 - x)
10 - x
10 - x
x
x
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
Problem #8
MATH is inscribed in the circle.
Angle M has a measure of 78 degrees.
Find the measure of angle T.
M
A
H
T
Solution to #8
Opp. Angles of inscribed quadrilaterals are
supp.
Measure of Angle T = 180 – 78 = 102о
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.
30
20cm60
120
C
B
A
Solution to #10
14 – x + 12 – x = 4
26 – 2x = 4
22 = 2x
x = 11
So BD = 14 – x = 312 - x
12 - x
14 - x
14 - x
xx
CDB
A
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 #13Two 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.
Problem #15Two secants drawn to a circle from an external point intercept arcs that are 122° and 68°. Find the measure of the secant-
secant angle.
P
122°
68°
Problem #17A central angle intercepts an arc that is 5/12
of the circle. Find the measure of angle x.
512
of circle O
O x
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 #18If PA and PB are tangent to circle O at A
and B, PA=24, and PO=26, find
perimeter of quadrilateral PAOB.
P
A
B
O
Solution to #18
• OA is perpendicular to PA 5, 12, 13 right triangle.
• OA = 10 and PB = 24
• 10 + 10 + 24 + 24 = 68
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.
Solution to #21
Parallelogram inscribedis a rectangle.
Diameter = 26 radius = 13
Area = (132) = 169
10
24
Problem #22
AB
C
•
•
•
•D
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).
Solution to #22
E
Rt. Triangle is 5, 12, 13 soAE = 12(3) = 36 in. Sothen CD = 36 in.
15 in
5 in 5 in
39 in.
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?
60°P
Solution to #23
30 6025 in
If P = 60 , then mAB = 120 ,so ACB = 120 . PC bisectsACB so ACP = 60 . Wehave a 30-60-90 triangle withx = 25 in.
PC = 50in.
B
C
A
P