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prove that D is circumcenter of MNK

Source: JBMO Shortlist 2017 G2

July 25, 2018
geometryCircumcenterequal anglescircumcircle

Problem Statement

Let ABCABC be an acute triangle such that ABAB is the shortest side of the triangle. Let DD be the midpoint of the side ABAB and PP be an interior point of the triangle such that ∠CAP=∠CBP=∠ACB\angle CAP = \angle CBP = \angle ACB. Denote by M and NN the feet of the perpendiculars from PP to BCBC and ACAC, respectively. Let pp be the line through M M parallel to ACAC and qq be the line through NN parallel to BCBC. If pp and qq intersect at KK prove that DD is the circumcenter of triangle MNKMNK.
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