Question 8
Let $[AB]$ be the diameter of a semicircle on which two points $C$ and $D$ are taken. Let $S$ be the intersection of $(AC)$ and $(BD)$, and $T$ the foot of the perpendicular from $S$ to $[AB]$.
Prove that $(ST)$ is the bisector of the angle $\widehat{CTD}$.
Prove that $(ST)$ is the bisector of the angle $\widehat{CTD}$.