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3 right angles, 2 of them by the altiudes

Source: 2012 Sharygin Geometry Olympiad Final Round 8.7

August 3, 2018
geometryaltitudes

Problem Statement

The altitudes AA1AA_1 and CC1CC_1 of an acute-angled triangle ABCABC meet at point HH. Point QQ is the reflection of the midpoint of ACAC in line AA1AA_1, point PP is the midpoint of segment A1C1A_1C_1. Prove that ∠QPH=90o\angle QPH = 90^o.
(D.Shvetsov)
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