# SOLUTION: A central angle intercepts an arc of a circle equal in length to a diameter of the circle, find the measure of the central triangle in radians.

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 Question 385197: A central angle intercepts an arc of a circle equal in length to a diameter of the circle, find the measure of the central triangle in radians. Answer by Edwin McCravy(8880)   (Show Source): You can put this solution on YOUR website!A central angle intercepts an arc of a circle equal in length to a diameter of the circle, find the measure of the central angle in radians. ```By definition, a central angle which intercepts an arc of a circle equal in length to a radius has a measure of 1 radian. Since a diameter is twice a radius, a central angle intercepts an arc of a circle equal in length to a diameter of the circle has a measure of two radians. The picture on the left below is a central angle which intercepts an arc of the circle equal in length to a radius and thus has a measure of 1 radian. The picture on the right below is your problem. It is a central angle which intercepts an arc of a circle equal in length to a diameter and thus has a measure of 2 radians. The green arc on the left is equal in length to 1 radius, and measures 1 radian. The green arc on the right is equal in length to 1 diameter, or 2 radii, and therefore measures 2 radians. Edwin```