MathDB
Parallel

Source: Chinese TST

April 4, 2008
geometrycircumcircleperpendicular bisectorpower of a pointradical axisgeometry proposed

Problem Statement

Let P P be the the isogonal conjugate of Q Q with respect to triangle ABC ABC, and P,Q P,Q are in the interior of triangle ABC ABC. Denote by O1,O2,O3 O_{1},O_{2},O_{3} the circumcenters of triangle PBC,PCA,PAB PBC,PCA,PAB, O1′,O2′,O3′ O'_{1},O'_{2},O'_{3} the circumcenters of triangle QBC,QCA,QAB QBC,QCA,QAB, O O the circumcenter of triangle O1O2O3 O_{1}O_{2}O_{3}, O′ O' the circumcenter of triangle O1′O2′O3′ O'_{1}O'_{2}O'_{3}. Prove that OO′ OO' is parallel to PQ PQ.
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