MathDB
Two circles

Source: Taiwan NMO 2006

March 21, 2006
geometrycircumcircleangle bisectorgeometry proposed

Problem Statement

P,QP,Q are two fixed points on a circle centered at OO, and MM is an interior point of the circle that differs from OO. M,P,Q,OM,P,Q,O are concyclic. Prove that the bisector of ∠PMQ\angle PMQ is perpendicular to line OMOM.
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