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Math Help - Prove a central angle is twice the measure of an inscribed angle

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    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!
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    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.
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    Quote Originally Posted by IIuvsnshine View Post
    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.
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    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
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    how to insert a image
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  6. #6
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    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
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