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.
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(20055) (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
