Question 94
Let $ABC$ be a triangle with $AB = AC$ and $M$ is the midpoint of the altitude $AD$. Consider $(\omega)$ as the circle of center $M$ and tangent to $AB$, $AC$. From some point $T$ on the line $BC$ (outside triangle $ABC$), construct two tangents of $(\omega)$ and they cut $AB$ at $P$, $Q$, cut $AC$ at $R$, $S$. Prove that $PQ = RS$.