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Turkey NMO 2001 Problem 1

Source: Turkey NMO 2001 Problem 1

September 30, 2011
geometrycircumcircletrapezoidgeometry proposed

Problem Statement

Let ABCDABCD be a convex quadrilateral. The perpendicular bisectors of the sides [AD][AD] and [BC][BC] intersect at a point PP inside the quadrilateral and the perpendicular bisectors of the sides [AB][AB] and [CD][CD] also intersect at a point QQ inside the quadrilateral. Show that, if ∠APD=∠BPC\angle APD = \angle BPC then ∠AQB=∠CQD\angle AQB = \angle CQD
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