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PQ // CD if <A=<C All-Russian MO 2005 Regional (R4) 8.6

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August 26, 2024
geometryangle bisector

Problem Statement

In quadrilateral ABCDABCD, angles AA and CC are equal. Angle bisector of BB intersects line ADAD at point PP. Perpendicular on BPBP passing through point AA intersects line BCBC at point QQ. Prove that the lines PQPQ and CDCD are parallel.
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