Question 79
Points $A$, $B$, and $C$ lie on a circle with centre $M$. The reflection of point $M$ in the line $AB$ lies inside triangle $ABC$ and is the intersection of the angular bisectors of angles $A$ and $B$. (The angular bisector of an angle is the line that divides the angle into two equal angles.) Line $AM$ intersects the circle again in point $D$.
Show that $|CA| \cdot |CD| = |AB| \cdot |AM|$.
Show that $|CA| \cdot |CD| = |AB| \cdot |AM|$.