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Asian Pacific Mathematical Olympiad 2010 Problem 1

Source:

May 7, 2010
geometrycircumcircleperpendicular bisectorgeometry proposed

Problem Statement

Let ABCABC be a triangle with ∠BAC≠90∘.\angle BAC \neq 90^{\circ}. Let OO be the circumcenter of the triangle ABCABC and Γ\Gamma be the circumcircle of the triangle BOC.BOC. Suppose that Γ\Gamma intersects the line segment ABAB at PP different from BB, and the line segment ACAC at QQ different from C.C. Let ONON be the diameter of the circle Γ.\Gamma. Prove that the quadrilateral APNQAPNQ is a parallelogram.
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