KöMaL 2024 B5360

The largest angle of scalene triangle $ABC$ is at vertex $C$. Let $T$ denote the foot of altitude from vertex $C$, and let the angle bisector from vertex $C$ intersect side $AB$ at point $F$. Prove that $\frac{AT}{TB}=\bigg(\frac{AF}{FB}\bigg)^2$ if and only if $\angle ACB =90^\circ$.