Problem

Source: Indian IMOTC 2013, Team Selection Test 1, Problem 2

Tags: geometry, geometric transformation, reflection, circumcircle, trigonometry, parallelogram, homothety



In a triangle $ABC$, with $\widehat{A} > 90^\circ$, let $O$ and $H$ denote its circumcenter and orthocenter, respectively. Let $K$ be the reflection of $H$ with respect to $A$. Prove that $K, O$ and $C$ are collinear if and only if $\widehat{A} - \widehat{B} = 90^\circ$.