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Korea Second Round 2011

Source: Korea Second Round 2011 #1

August 21, 2011
geometryparallelogramrhombusgeometry unsolved

Problem Statement

Two circles O,O′ O, O' having same radius meet at two points, A,B(A≠B) A,B (A \not = B) . Point P,Q P,Q are each on circle O O and O′ O' (P≠A,B Q≠A,B)(P \not = A,B ~ Q\not = A,B ). Select the point R R such that PAQR PAQR is a parallelogram. Assume that B,R,P,Q B, R, P, Q is cyclic. Now prove that PQ=OO′ PQ = OO' .
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