Let $ABC$ be an acute triangle where $AC > BC$. Let $T$ denote the foot of the altitude from vertex $C$, denote the circumcentre of the triangle by $O$. Show that quadrilaterals $ATOC$ and $BTOC$ have equal area.
Source: 2020 Dürer Math Competition Finals E1. 1
Tags: geometry, equal area, equal areas
Let $ABC$ be an acute triangle where $AC > BC$. Let $T$ denote the foot of the altitude from vertex $C$, denote the circumcentre of the triangle by $O$. Show that quadrilaterals $ATOC$ and $BTOC$ have equal area.