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China Mathematical Olympiad 1990 problem1

Source: China Mathematical Olympiad 1990 problem1

October 18, 2013
geometry unsolvedgeometry

Problem Statement

Given a convex quadrilateral ABCDABCD, side ABAB is not parallel to side CDCD. The circle O1O_1 passing through AA and BB is tangent to side CDCD at PP. The circle O2O_2 passing through CC and DD is tangent to side ABAB at QQ. Circle O1O_1 and circle O2O_2 meet at EE and FF. Prove that EFEF bisects segment PQPQ if and only if BC∥ADBC\parallel AD.
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