Thread: 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!

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.

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.

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

how to insert a image

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