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tangent of (DP_1A_1) // BC, cyclic ABCD

Source: 2022 Sharygin CR p5

March 6, 2022
geometryparallelcyclic quadrilateral

Problem Statement

Let the diagonals of cyclic quadrilateral ABCDABCD meet at point PP. The line passing through PP and perpendicular to PDPD meets ADAD at point D1D_1, a point A1A_1 is defined similarly. Prove that the tangent at PP to the circumcircle of triangle D1PA1D_1PA_1 is parallel to BCBC.
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