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Orthocentre's unique property

Source: Tournament of Towns, Fall 2002, Junior A Level, P4

May 17, 2014
geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

Point PP is chosen in the plane of triangle ABCABC such that ∠ABP\angle{ABP} is congruent to ∠ACP\angle{ACP} and ∠CBP\angle{CBP} is congruent to ∠CAP\angle{CAP}. Show PP is the orthocentre.
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