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Iran geometry

Source: Iran MO 3rd round 2019 finals - Geometry P2

August 14, 2019
geometrycircumcircle

Problem Statement

In acute-angled triangle ABCABC altitudes BE,CFBE,CF meet at HH. A perpendicular line is drawn from HH to EFEF and intersects the arc BCBC of circumcircle of ABCABC (that doesn’t contain AA) at KK. If AK,BCAK,BC meet at PP, prove that PK=PHPK=PH.
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