KöMaL 2012 B4474

The points $K$, $L$, $M$ and $N$, respectively, lie on sides $AB$, $BC$, $CD$ and $DA$ of a square ABCD . Given that $\angle$ KLA =$\angle$ LAM =$\angle$ AMN $=45^o$, prove that $KL^2$+$AM^2$=$LA^2$+$MN^2$.