# Thread: Prove a central angle is twice the measure of an inscribed angle

1. ## Prove a central angle is twice the measure of an inscribed angle

We are given a circle centered at O, and points P, Q, and R on the circle. We want to prove the central angle POR is twice the measure of the inscribed angle PQR.

I do not know how to set up the steps for the proof!! Help, please if you can!

2. First prove an easier result. If P and R are a diameter, i.e. when the line segment joining the two points passes through the center.

3. Originally Posted by IIuvsnshine
We are given a circle centered at O, and points P, Q, and R on the circle. We want to prove the central angle POR is twice the measure of the inscribed angle PQR.

I do not know how to set up the steps for the proof!! Help, please if you can!
Draw the line from Q to O, and continue it beyond O to some point S. Look at the angles in the (isosceles) triangles PQO and RQO, and see if that tells you something about the angles POS and ROS.

4. ## central angle/inscribed angle

you have an answer for one special case.here is another.strike a 60 degree arc of the circle. bisect it. mark the radii intersections PQR. O is the center.PQR inscribed angle is 120 degrees and the central is60 degrees

bj

5. how to insert a image

6. ## central angle-inscribed angle of circle

I do not have any way to create images and would like to know wirhout adding new programs'

Relative to the original problem a central angle equals the arc, the inscribed angle of the same arc is half the arc.The wording of the problem was confusing since it was not specifed thatQ was a point outside PR

I assumed a case where Q was the center of PR and then made an error in the answer. the inscribed angle should be 150 degrees

bj