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Triangle and circle

Source: Pre-VMO 2012 - Round 2 - Problem 3

December 25, 2011
geometrycircumcircleperpendicular bisectorpower of a pointradical axisgeometry proposed

Problem Statement

Let ABCABC be a triangle with height AHAH. PP lies on the circle over 3 midpoint of AB,BC,CAAB,BC,CA (Pāˆ‰BCP \notin BC). Prove that the line connect 2 center of (PBH)(PBH) and (PCH)(PCH) go through a fixed point. (where (XYZ)(XYZ) be a circumscribed circle of triangle XYZXYZ)
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