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Equal angles

Source: All Russian Olympiad - Problem 11.7

May 10, 2009
geometryparallelogramcircumcircletrigonometryfunction

Problem Statement

Let be given a parallelogram ABCD ABCD and two points A1 A_1, C1 C_1 on its sides AB AB, BC BC, respectively. Lines AC1 AC_1 and CA1 CA_1 meet at P P. Assume that the circumcircles of triangles AA1P AA_1P and CC1P CC_1P intersect at the second point Q Q inside triangle ACD ACD. Prove that \angle PDA \equal{} \angle QBA.
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