Question 126
Points $A$, $B$, $C$ are given on a semicircle. The line which is tangent to the semicircle at $A$ intersects the line of the diameter at $M$, and the line which is tangent to the semicircle at $B$ intersects the line of the diameter at $N$. The line which passes through $A$ and is perpendicular to the diameter intersects $NC$ at $R$, and the line which passes through $B$ and is perpendicular to the diameter intersects $MC$ at $S$. The line $RS$ intersects the line of the diameter at $Z$. Show that $ZC$ is tangent to the semicircle.