Name: ____________________________ Class: ____________
Circle Geometry Practice
Tangent Radius Property
1. O is the center of the circle. PT is a tangent line. P is the point
of tangency. What is the value of x° and y°?
2. O is the center of the circle. PT is a tangent line. P is the point
of tangency. What is the length of PT?
3. Point O is the center of the circle. P is the point of tangency.
What is the value of x° and y°?
4. Point O is the center of the circle. P is the point of tangency.
What is the value of x° and y°?
5. Point O is the center of the circle. P is the point of tangency.
Determine the value of a.
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Name: ____________________________ Class: ____________
6.
a. What is the measure of ∠CEF?
b. What is the measure of ∠ECF?
c. What is the measure of ∠DCE?
d. What is the measure of ∠CED?
e. What is the measure of ∠ECD?
7. Line segment JK is a tangent to the circle at point H. GH is the
diameter and ∠CGL = 10°.
a. What is the measure of ∠GCL?
b. What is the measure of ∠JCH?
c. What is the measure of ∠JHG?
d. What is the measure of ∠CJK?
8. AB is tangent to the circle at point B. BD is a diameter of the
circle. AB = 6 m , AD = 10 m ∆BCE is an equilateral triangle.
a. What is the length of the diameter, BD?
b. What is the length of the radius?
c. What is the length of BE?
d. What is the measure of ∠BEC
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Name: ____________________________ Class: ____________
9. Line EG is tangent to the circle. Find the length of x in the
diagram. Write your answer to the nearest tenth.
10.
a. What is the measure of ∠BDC
b. What is the measure of ∠DCB
c. What is the measure of ∠DCE
d. What is the measure of ∠CED
e. What is the measure of ∠EDC
11.
a. What is the length of BD ?
b. What is the length of BC ?
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Name: ____________________________ Class: ____________
12. PQ is tangent to the circle at point Q. QR is a diameter of the
circle. PQ = 9 mm; PR = 41 mm ∆QCS is an equilateral
triangle.
a. What is the length of the diameter?
b. What is the length of the radius?
13. Point S is a point of tangency and O is the center of the circle.
Determine the values of a and b to the nearest tenth.
14. A circular mirror with radius 20 cm hangs by a wire from a
hook. The wire is 30 cm long and is a tangent to the mirror in
two places. How far above the top of the mirror is the hook?
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Name: ____________________________ Class: ____________
Chord Properties
1. Radius CD bisects chord AB. Chord AB = 8 cm and radius = 5
cm. What is the length of line segment CE?
2. The radius of the circle is 17 m. The radius CD is
perpendicular to the chord AB. CE measures 8 m. What is the
length of chord AB?
3. Find the length of x.
4. Point 0 is the center of the circle. Determine each value of x° and y°.
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Name: ____________________________ Class: ____________
5. Point O is the center of the circle.
a. Determine the length of HK.
b. Determine the length of JK.
c. Determine the length of HJ.
6. Point O is the center of the circle. Determine the value of b.
7. Point O is the center of the circle. Determine the value of b.
8. Point O is the center of the circle. Determine the value of r.
(Which extra line segments do you need to draw first?)
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Name: ____________________________ Class: ____________
9. Point O is the center of the circle. Determine the value of r.
(Which extra line segments do you need to draw first?)
10. Point O is the center of the circle. Determine the value of s.
11. Point O is the center of the circle. Determine the value of s.
12. A pedestrian underpass is constructed beneath a roadway
using a cylindrical pipe with a radius 1.8 m. The bottom of
the pipe will be filled and paved. The headroom at the center
of the path is 2.8 m. How wide is the path.?
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Name: ____________________________ Class: ____________
Angle Properties
1. Point C is the center of the circle. ∠AEB = 35º
a. What is the measure of ∠ADB?
b. What is the measure of ∠ACB?
2. Point C is the center of the circle.
a. What is the measure of ∠FJG?
b. What is the measure of ∠FCG?
3. Point C is the center of the circle. ∠DAB = 55º
a. What is the measure of ∠DEB?
b. What is the measure of ∠DCB?
4. Point C is the center of the circle. The central angle is ∠ACB.
AB is the diameter. Chord AD = 12 cm and chord BD = 5 cm.
a. What is the measure of ∠ADB?
b. What is the length of diameter AB?
5. Point C is the center. ∠KJM = 15° and ∠JML = 24°.
a. What is the measure of ∠KLM?
b. What is the measure of ∠JKL?
c. What is the measure of ∠JCL?
d. What is the measure of ∠KCM?
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Name: ____________________________ Class: ____________
6. Point O is the center of the circle. Determine the values of x°
and y°.
7. In the diagram, ∠BAD = 34° and ∠ADE = 56°
a. What is the measure of ∠ABE?
b. What is the measure of ∠AGB?
8. Can you use the Pythagorean relationship to find the length
of AB. Will this work? Give 1 reason for your answer.
9. Rectangle ABCD has its vertices on the circle with a radius of
8.5 cm. The width of the rectangle is 10.0 cm. What is the
length to the nearest tenth?
10. Water is flowing through a pipe with a radius of 14 cm. The
maximum depth of the water is 9 cm. What is the width, PQ,
at the surface of the water.
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