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equal angles starting with a parallelogram ABCD with <DAC=90^o

Source: Iranian Geometry Olympiad 2018 IGO Intermediate p5

September 19, 2018
geometryparallelogramequal anglescircumcircle

Problem Statement

Suppose that ABCDABCD is a parallelogram such that ∠DAC=90o\angle DAC = 90^o. Let HH be the foot of perpendicular from AA to DCDC, also let PP be a point along the line ACAC such that the line PDPD is tangent to the circumcircle of the triangle ABDABD. Prove that ∠PBA=∠DBH\angle PBA = \angle DBH.
Proposed by Iman Maghsoudi
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