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If tangents at C,D meet at P then PC=PE

Source: Polish Second Round 2009

August 4, 2011
geometrycyclic quadrilateralgeometry unsolved

Problem Statement

ABCDABCD is a cyclic quadrilateral inscribed in the circle Γ\Gamma with ABAB as diameter. Let EE be the intersection of the diagonals ACAC and BDBD. The tangents to Γ\Gamma at the points C,DC,D meet at PP. Prove that PC=PEPC=PE.
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