Proving a Pythagorean Relation in an Isosceles Right Triangle

In an isosceles right triangle $ABC$ with $AB$ as the hypotenuse, select points $M$ and $K$ on $AB$ such that $K$ lies between $M$ and $B$, and the angle $\angle MCK = 45^\circ$. Prove that:
$MK^2 = AM^2 + KB^2.$