Question 93
A point $D$ is chosen on the side $BC$ of the triangle $ABC$. The line tangent to the incircles of the triangles $ABD$ and $ADC$ and different from $BC$ and $AD$ intersects the segment $AD$ at $T$. If $AB=40\ \mathrm{cm}$, $AC=50\ \mathrm{cm}$ and $BC=60\ \mathrm{cm}$, determine the length of $AT$.
