Honors Geometry
Ch. 10 Finals Review
Name______KEY_______________
Date_____________Period________
In problems 1-7, refer to the diagram and information given.
Given:
Circle O
Tangent EH , secants AC and AD
m DEH =50
m BCG =15
arc CD=60


arc FE=100


1. Find m arc DE
100o
60o
1. ___100____
2. Find m FDE
2. ___50______
3. Find m arc BF
3. ___30______

4. Find m arc CB 70o
4. ___70______
o
30
5. Find m CDF
5. ___50______
o
100
6. Find m A
6. ___15______

7. Find m CGD

7. ___45______
30o

8.
8
9. Given: RC=12
OC=8
RK is tangent
to the circle
Find RK.
115o
65

10.
11.
6
x2 = 4(12)
6
2
x=4
40 = 2(x+2)
40 = 2x + 4
36 = 2x
12.
x = 18
x=5
12
x2 = 4√3
In problems 13-15, use the diagram.
13. Find the measure of arc AB.
60o
60
14. Find the circumference of
circle O.
2𝜋r = 2𝜋15 = 30𝜋
15. Find the length of arc AB.
60
1
2𝜋r360 = 2𝜋15 6 = 5𝜋
16. Find DF.
17. Given: Tangent Circle A, B, C,
AB=7, BC=9, AC=12
Find: The radii of the three
circles (This is a walk-around
problem)
19
16
7-x
7-x
B=2
A=5
C=7
12-7-x
x
x
18. Find x.
9-x
19. Find y.
2(12) = 3(3 + y)
24 = 9 + 3y
y=5
3
x2 = 3(18)
x = 3√3
20. Find the measure of arc AB
21. Find the measure of arc QUA.
Arc QUA = 300o
30
x
30
1
(𝑥 − 15)
2
x = 75
60o
22. Given: Circle O and P are externally tangent.
OA=10, PB=2
Find: The length of common external
tangent AB.
23. Find, to the nearest meter, the
length of fencing needed to 12𝜋 + 100
or
surround the racetrack.
~ 138
4√5
Complete #24 – 29 using the diagram at right.
24. If m arc AB=120 and m arc CD=100, then m 2=____110________.
25. If m 4 =60, then m 1=______60_______.
26. If m arc AB=110 and m arc BC=140, then m 3=_____55_______.

27. If AB  AC and m arc AB=140, then m 5 =_____40_____.


28. If m 2=85 and m arc DC=65, then m arc AB=____105______.

29. If DB is a diameter, then m BCD=____90______.


Find the value of x in each of the following circles.


30.
31.
32.
x = ____40______
x = ___20______
x = ____90______
33.
34.
35.
x = _____110_____
x = ____x = 6_____
x = ____8_______
36.
37.
x = _____12_____
4(x + 4) = 64
x = ____6______ or x = ___4_______
24 = x(10-x)
24 = 10x – x2
x2 – 10x + 24
(x - 6)(x – 4)
38. Find the circumference of a circle in which an 30 cm chord is 8 cm from the center.
30
8
17
39a. Find x.
2𝜋𝑟 = 34𝜋
39b. Find x.
x=6
x = 13
40. Find x.
(hint: walk around problem)
41. Circle O is inscribed in PQR. PQ=10,
QR=13, and PR=21. Find PT.
(hint: walk around problem)
10-x
x = 17
PT = 9
13-x
10-x
x
x
42. AC=9, AB=7, CB=8.
Find the length of the radius of the
largest circle.
13-x
43. Circle O with radius 10 and circle P with
radius 4. The length of the common
external tangent segment is 16.
Find the distance between the two circles.
5
14 - 2√73
44. Two circles with radii 9 cm and 6 cm
are 4 cm apart. Find the length of the
common internal tangent.
2√34
45. Find PQ
30