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silk road 2018 geometry

Source: SRMC 2018 P1

August 30, 2018
geometryaltitudes

Problem Statement

In an acute-angled triangle ABCABC on the sides ABAB, BCBC, ACAC the points HH, LL, KK so that CH⊥ABCH \perp AB, HL∥ACHL \parallel AC, HK∥BCHK \parallel BC. Let PP and QQ feet of altitudes of a triangle HBLHBL, drawn from the vertices HH and BB respectively. Prove that the feet of the altitudes of the triangle AKHAKH, drawn from the vertices AA and HH lie on the line PQPQ.
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