To review these concepts, go to Circle Word Problems Study Guide.
Circle Word Problems Practice Questions
Practice 1
Problems
Use the following figure to identify the basic parts of the circle.
Center _____ Radius _____ Diameter _____ Central Angle _____ Inscribed Angle _____
Solutions
Center Radius Diameter Central Angle Inscribed Angle
Practice 2
Problems
 The measure of a central angle is 50°. What is the measure of the arc it intercepts?
 The measure of an arc on a circle is 25°. What is the measure of the central angle that intercepts it?
 The measure of an inscribed angle is 40°. What is the measure of the arc on the circle that it intercepts?
 The measure of an arc on a circle is 34°. What is the measure of the inscribed angle that intercepts it?
Solutions
 Read and understand the question. This question is looking for the measure of the arc intercepted by a central angle.
 Read and understand the question. This question is looking for the measure of the central angle when the measure of the intercepted arc is known. Make a plan. The measure of an arc is equal to the measure of the central angle that intercepts it. Use the measure of the arc to find the measure of the central angle.
 Read and understand the question. This question is looking for the measure of the arc intercepted by an inscribed angle.
 Read and understand the question. This question is looking for the measure of the inscribed angle when the measure of the intercepted arc is known.
Make a plan. The measure of an arc is equal to the measure of the central angle that intercepts it. Find the measure of this angle to find the measure of the arc.
Carry out the plan. The measure of the central angle is 50°, so the measure of the arc is also 50°.
Check your answer. The measure of the arc is the same number of degrees as the central angle. This result is checking.
Carry out the plan. The measure of the arc is 25°, so the measure of the central angle is also 25°.
Check your answer. The measure of the arc is the same number of degrees as the central angle. This result is checking.
Make a plan. The measure of the arc is equal to twice the measure of the inscribed angle that intercepts it. Find the measure of this angle and multiply by 2 to find the measure of the arc.
Carry out the plan. The inscribed angle measures 40°. Multiply 2 × 40 = 80. The intercepted arc measures 80°.
Check your answer. To check the solution, divide the result by 2 to find the measure of the inscribed angle: 80 ÷ 2 = 40° in the inscribed angle. This answer is checking.
Make a plan. The measure of the inscribed angle is half the measure of the arc it intercepts. Find the measure of this angle by dividing the measure of the arc by 2.
Carry out the plan. The intercepted arc measures 34°. Divide 34 ÷ 2 = 17. The inscribed angle measures 17°.
Check your answer. To check the solution, multiply the result by 2 to find the measure of the intercepted arc: 17 × 2 = 34° in the intercepted arc. This answer is checking.

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