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2008 ToT Spring Senior O P3 equal segments, circumcircle related, right triangle

Source:

February 26, 2020
geometrycircumcircleequal segmentsright triangle

Problem Statement

In triangle ABC,∠A=90oABC, \angle A = 90^o. MM is the midpoint of BCBC and HH is the foot of the altitude from AA to BCBC. The line passing through MM and perpendicular to ACAC meets the circumcircle of triangle AMCAMC again at PP. If BPBP intersects AHAH at KK, prove that AK=KHAK = KH.
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