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Nice orthocenter config

Source: India IMOTC 2024 Day 4 Problem 3

May 31, 2024
geometry

Problem Statement

Let ABCABC be an acute-angled triangle with AB<ACAB<AC, and let O,HO,H be its circumcentre and orthocentre respectively. Points Z,YZ,Y lie on segments AB,ACAB,AC respectively, such that ∠ZOB=∠YOC=90∘.\angle ZOB=\angle YOC = 90^{\circ}. The perpendicular line from HH to line YZYZ meets lines BOBO and COCO at Q,RQ,R respectively. Let the tangents to the circumcircle of △AYZ\triangle AYZ at points YY and ZZ meet at point TT. Prove that Q,R,O,TQ, R, O, T are concyclic.
Proposed by Kazi Aryan Amin and K.V. Sudharshan
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