ITOT 42 Spring 2021 - Junior O (THCS, Basic) - additive practice Question 2

Let $AX$ and $BZ$ be altitudes of triangle $ABC$, and let $AY$ and $BT$ be its angle bisectors. Given $\angle XAY=\angle ZBT$, must triangle $ABC$ be isosceles? (4 points)



Editorial illustration; no extra mathematical assumptions.