Problem

Source: 42nd International Tournament of Towns, Junior O-Level P2, Spring 2021

Tags: geometry, Tournament of Towns



Let $AX$ and $BZ$ be altitudes of the triangle $ABC$. Let $AY$ and $BT$ be its angle bisectors. It is given that angles $XAY$ and $ZBT$ are equal. Does this necessarily imply that $ABC$ is isosceles? The Jury