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Math Help - triangle orthocenter and circumcircle

  1. #1
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    triangle orthocenter and circumcircle

    Here is my problem:

    Given an arbitrary triangle ABC, let A' denote the diametral opposite of A in the circumcircle of triangle ABC. If H is the orthocenter of triangle ABC, show that segments HA' and BC bisect each other.

    I tried to proceed by proving triangle CQA' and triangle BQH (where Q is the intersection of HA' and BC) are congruent, which would give me the result I need. But I couldn't see how to get there.

    Thanks!

    I'm trying to help in this thread, but I got stuck.
    http://www.mathhelpforum.com/math-he...dilations.html
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  2. #2
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    Let O be the center of the circle. If you can show that OQB is a right angle, then triangles OQB and OQC are congruent, which means QB is the same length as QC.
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  3. #3
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    Thanks, but I got the solution by another method - see the original thread:
    http://www.mathhelpforum.com/math-he...dilations.html
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