DK-GEORGMOHR 2022 Problem 3

The square $ABCD$ has side length $1$ . The point $E$ lies on the side $CD$ . The line through $A$ and $E$ intersects the line through $B$ and $C$ at the point $F$ . Prove that $$\frac{1}{|AE|^2}+\frac{1}{|AF|^2}= 1.$$