Question 10
Let $\omega_{1}$, $\omega_{2}$ be two circles tangent to each other at a point $T$, such that $\omega_{1}$ is inside $\omega_{2}$. Let $M$ and $N$ be two distinct points on $\omega_{1}$, different from $T$. Let $[AB]$ and $[CD]$ be two chords of the circle $\omega_{2}$ passing through $M$ and $N$ respectively. Assume that the segments $[BD]$, $[AC]$ and $[MN]$ intersect at a point $K$.
Prove that $(TK)$ is the bisector of the angle $\widehat{MTN}$.
Prove that $(TK)$ is the bisector of the angle $\widehat{MTN}$.