Question 4
Let $\overline{AB}$ be a chord of a circle, parallel to its diameter $\overline{MN}$. Let $t$ be the tangent of that circle in $M$ and let $C, D$ be the intersections of the lines $NA, NB$ with $t$, respectively. Prove
$$
|MC| \cdot |MD| = |MN|^2.
$$
$$
|MC| \cdot |MD| = |MN|^2.
$$