Introduction to Circle Word Problems
Numbers are intellectual witnesses that belong only to mankind.
—HONORE DE BALZAC (1799–1850)
This lesson includes circle word problems while reviewing the basic parts and formulas involved with circles.
Tip:Remember that a circle is the set of points that is an equal distance from a single point. The circle is named by the center point. The total number of degrees in any circle is 360. 
Basic Parts of Circles
There are some basic parts of the circle that are necessary to know when you are applying the formulas related to circles. Each of these important parts of circle B is shown in the following figure. The point B is the center of the circle.
Radius: The distance from the center of a circle to a point on the circle. The plural of radius is radii. The radii in the figure are , , and .
Chord: A line segment whose endpoints are on the circle. Chords and are shown in the figure.
Diameter: A chord that goes through the center of a circle. The diameter is shown in the figure.
Arc: A section of the circle. The symbol for an arc is a curved line above the letters of the arc. Arc is shown in the figure.
Central Angle: An angle whose vertex is the center of the circle. The measure of the central angle is the same as the measure of the arc it intercepts. The angle in the figure is a central angle.
Inscribed Angle: An angle whose vertex is on the circle. The measure of an inscribed angle is equal to half of the arc it intercepts. The angle in the figure is an inscribed angle.
Questions About Special Angles and Circles
There are some special angles that are located within circles and are related to the center of the circle and the chords of the circle. Two of these special angles are central angles and inscribed angles.
Example 1
In this figure the measure of central angle is 30°. What is the measure of the intercepted arc ?
Read and understand the question. This question is looking for the measure of the arc intercepted by a central angle
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 30°, so the measure of the arc is also 30°.
Check your answer. The measure of the arc is the same number of degrees as the central angle. This result is checking.
Example 2
In this figure the measure of inscribed angle is 20°. What is the measure of the intercepted arc ?
Read and understand the question. This question is looking for the measure of the arc intercepted by an inscribed angle.
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 two to find the measure of the arc.
Carry out the plan. The inscribed angle measures 20°. Multiply 2 × 20 = 40. The intercepted arc measures 40°.
Check your answer. To check the solution, divide the result by 2 to find the measure of the inscribed angle: 40 ÷ 2 = 20° in the inscribed angle. This answer is checking.
Tip:Remember that the measure of a central angle is equal to the measure of the intercepted arc, and the measure of an inscribed angle is half the measure of the intercepted arc. 

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