BALTIC-WAY 2001 Problem 7

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

$$|A B| \cdot|A M|+|A D| \cdot|A N|=|A K| \cdot|A C| .$$