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Prove perpendicular

Source: APMO 2000

April 1, 2006
ratiogeometrycircumcircletrigonometryangle bisectorperpendicular bisector

Problem Statement

Let ABCABC be a triangle. Let MM and NN be the points in which the median and the angle bisector, respectively, at AA meet the side BCBC. Let QQ and PP be the points in which the perpendicular at NN to NANA meets MAMA and BABA, respectively. And OO the point in which the perpendicular at PP to BABA meets ANAN produced. Prove that QOQO is perpendicular to BCBC.
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