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Thread: Circle geo helpp

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    Junior Member supR's Avatar
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    Circle geo helpp

    Thanks in advance

    Question 13 from yr 12 3u, 9C

    13.a - Prove that if two chords of a circle bisect each other, then they are both diameters.


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    Re: Circle geo helpp

    Quote Originally Posted by supR View Post
    Thanks in advance

    Question 13 from yr 12 3u, 9C

    13.a - Prove that if two chords of a circle bisect each other, then they are both diameters.


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    Let one chord be AB, and one be CD with the midpoints of both as M

    AM x BM = CM x DM (product of intercepts of chords)
    and AM = BM and CM = DM as they are both bisected
    AM^2 = CM^2
    AM = CM
    So AM = BM = CM = DM

    Hence these are all radii with M as the centre of the circle, hence both chords are diameters
    jazz519 and supR like this.
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