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X56 Jumpscare

Source: USEMO 2024/3

October 26, 2024
geometryUSEMOUSEMO 2024

Problem Statement

Let ABCABC be a triangle with incenter II. Two distinct points PP and QQ are chosen on the circumcircle of ABCABC such that ∠API=∠AQI=45∘. \angle API = \angle AQI = 45^\circ. Lines PQPQ and BCBC meet at SS. Let HH denote the foot of the altitude from AA to BCBC. Prove that ∠AHI=∠ISH\angle AHI = \angle ISH.
Matsvei Zorka
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