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Center of W_a,W_b, W_c are collinear.

Source: Iranian National Olympiad (3rd Round) 2003

January 24, 2009
geometrycircumcirclegeometry proposed

Problem Statement

Let ABC ABC be a triangle. Wa W_a is a circle with center on BC BC passing through A A and perpendicular to circumcircle of ABC ABC. Wb,Wc W_b,W_c are defined similarly. Prove that center of Wa,Wb,Wc W_a,W_b,W_c are collinear.
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