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concurrency inside a tangential wanted 2 perpendiculars, 1 angle bisector

Source: Switzerland - Swiss MO 2013 p10

July 16, 2020
geometryconcurrencyconcurrenttangential quadrilateralangle bisector

Problem Statement

Let ABCDABCD be a tangential quadrilateral with BC>BABC> BA. The point PP is on the segment BCBC, such that BP=BABP = BA . Show that the bisector of ∠BCD\angle BCD, the perpendicular on line BCBC through PP and the perpendicular on BDBD through AA, intersect at one point.
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