MathDB
Perpendicular

Source: Taiwan MO 2000, Indian TST 2011

May 22, 2010
geometrycircumcirclepower of a pointradical axis

Problem Statement

Let ABCABC be a triangle in which BC<ACBC<AC. Let MM be the mid-point of ABAB, APAP be the altitude from AA on BCBC, and BQBQ be the altitude from BB on to ACAC. Suppose that QPQP produced meets ABAB (extended) at TT. If HH is the orthocenter of ABCABC, prove that THTH is perpendicular to CMCM.
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