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Math Help - Triangle

  1. #1
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    Triangle

    Problem:

    H is the orthocenter of acute triangle ABC, from A, draw the two tangent lines AP and AQ of the circle whose diameter is BC, the points of tangency are P, Q respectively. Prove: P, H, Q are collinear.
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  2. #2
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    • Let \omega be the circle with diameter BC
    • Let B' & C' be the projections of B & C to \overline{AC} & \overline{AB} respectively.
    • In the cyclic quadrilateral BCB'C' with A\in\overline{BC'}\cap\overline{CB'} & H\in\overline{BB'}\cap\overline{CC'} yields that H is on the polar line of A\,\blacksquare
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