Circle quiz

Geometry – Circles

NJCTL.org

8. Find the value of 𝑧.

9. Find the value of 𝑤.

10. Find the value of 𝑡.

11. Find the value of 𝑗.

12. Find the value of 𝑏.

13. Use the information in the diagram to choose all possible values of 𝑥 and 𝑦.

a. 𝑥 = 30°, 𝑦 = 90°
b. 𝑥 = 50°, 𝑦 = 25°
c. 𝑥 = 40°, 𝑦 = 80°
d. 𝑥 = 100°, 𝑦 = 200°
e. 𝑥 = 44°, 𝑦 = 44°
f. 𝑥 = 15°, 𝑦 = 30°

𝑦°

z°

140°

w°

50°

110°

𝑥°

Geometry – Circles

NJCTL.org

Point M is the center of a circle. 𝐽𝐾̅̅̅ is the diameter of the circle. Point 𝐿 is a point on the

circle, different from 𝐽 and 𝐾

14. 𝐽𝐾 > 𝐾𝐿

a. Always
b. Sometimes
c. Never

15. 𝑚∠𝐿𝐾𝐽 = 90°

a. Always
b. Sometimes
c. Never

16. 𝑚∠𝐽𝐾𝐿 = 2(𝑚∠𝐿𝐽𝐾)

a. Always
b. Sometimes
c. Never

17. If 𝑚∠𝐿𝐽𝐾 = 23°, what is 𝑚∠𝐾𝑀𝐿?

a. 23°
b. 46°
c. 134°
d. 157°

18. A log with diameter 20” is floating in a river. If the height from the river to the top

of the log is 16”, what is the distance across the log at the water surface?

19. The arc of a circle has measure 22°and length 12 cm, what is the circle’s radius?

Log redrawn three
dimensionally

Front view of the log

NJCTL.org

20. A triangle is inscribed in circle creating three arcs. Two of the arcs are 140° and

150°, list the measures of the angles of the triangle from least to greatest.

21. In the diagram, 𝐴𝐵̅̅̅̅ 𝑎𝑛𝑑 𝐶𝐵

̅̅̅̅ 𝑎𝑟𝑒 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 𝑡𝑜 𝑐𝑖𝑟𝑐𝑙𝑒 𝐷 and 𝑚∠𝐷 = 130°

a. 𝐹𝑖𝑛𝑑 𝑚∠𝐵.

b. If 𝐴𝐷 = 6, what is the length of AEĈ ?

c. If 𝐴𝐵 = 5𝑥 + 16 and 𝐶𝐵 = 9𝑥 − 31, then find the value of 𝑥.

NJCTL.org

Circles Unit Re-Test
PMI Geometry

Name ________________________

1. If 𝑇𝐶 = 12, then 𝐴𝑀 = ?

a. 6
b. 12
c. 18
d. 24

2. If 𝑇𝐶 = 10 and 𝐽𝐻 = 6, how far is 𝐽𝐻̅̅̅̅

from the center?

a. 10
b. 9
c. 8
d. 4

3. JH̅̅̅ ∥ TC̅̅̅̅ and 𝑚𝐽𝐻̂ = 100°,𝑚𝐽𝑇̂ =

a. 40°
b. 50°
c. 60°
d. 70°

4. 𝑚∠𝐷𝐶𝐵 = 130°, 𝑚𝐵𝐴𝐷

̂ =

5. 𝑚∠𝐷𝐶𝐵 = 130°, find the measure of 𝐵𝐴̂ in radians

6. Find the value of 𝑥 .

7. Find the value of 𝑦 (circles are concentric).

40°

x°

C

NJCTL.org

8. Find the value of 𝑧.

9. Find the value of 𝑤.

10. Find the value of 𝑥.

11. Find the value of 𝑗.

12. Find the value of 𝑏.

13. Use the information in the diagram to choose all possible values of 𝑥 and 𝑦.

a. 𝑥 = 30°, 𝑦 = 60°
b. 𝑥 = 25°, 𝑦 = 25°
c. 𝑥 = 40°, 𝑦 = 80°
d. 𝑥 = 185°, 𝑦 = 370°
e. 𝑥 = 44°, 𝑦 = 22°
f. 𝑥 = 15°, 𝑦 = 30°

50°

z°

110°

50°

w°

b

4

5
7

𝑦°

𝑥°

NJCTL.org

Point 𝐶 is the center of a circle. 𝐴𝐵̅̅̅̅ is the diameter of the circle. Point 𝐷 is a point on

the circle, different from 𝐴 and 𝐵

14. 𝐴𝐷 > 𝐵𝐷

a. Always
b. Sometimes
c. Never

15. 𝑚∠𝐴𝐷𝐵 = 90°

a. Always
b. Sometimes
c. Never

16. 𝑚∠𝐴𝐷𝐵 = 2(𝑚∠𝐴𝐵𝐷)

a. Always
b. Sometimes
c. Never

17. If 𝑚∠𝐴𝐵𝐷 = 62°, what is 𝑚∠𝐴𝐶𝐷?

a. 28°
b. 56°
c. 62°
d. 124°

18. A log with diameter 24” is floating in a river. If the height from the river to the top

of the log is 18”, what is the distance across the log at the water surface?

19. The arc of a circle has measure 48° and length 20 cm, what is the circle’s radius?

Log redrawn three
dimensionally

Front view of the log

NJCTL.org

20. A triangle is inscribed in circle creating three arcs. Two of the arcs are 110° and

170°, list the measures of the angles of the triangle from least to greatest.

21. In the diagram, 𝐴𝐵̅̅̅̅ and 𝐶𝐵̅̅̅̅ are tangent to circle 𝐷 and 𝑚∠𝐷 = 140°

a. 𝐹𝑖𝑛𝑑 𝑚∠𝐵

b. If 𝐴𝐷 = 8, what is the length of AEĈ ?

c. If 𝐴𝐵 = 4𝑥 + 9 and 𝐶𝐵 = 10(𝑥 − 3), then find the value of 𝑥.