Question 21
Given a parallelogram $A B C D$. A circle passing through $A$ meets the line segments $A B$, $A C$ and $A D$ at inner points $M$, $K$, $N$, respectively. Prove that
$$
|A B| \cdot|A M|+|A D| \cdot|A N|=|A K| \cdot|A C| .
$$
$$
|A B| \cdot|A M|+|A D| \cdot|A N|=|A K| \cdot|A C| .
$$