UA-UMO 1999 Problem 97

Let $M$ be a fixed point inside a given circle. Two perpendicular chords $AC$ and $BD$ are drawn through $M$ , and $K$ and $L$ are the midpoints of $AB$ and $CD$ , respectively. Prove that the quantity $AB^2+CD^2-2KL^2$ is independent of the chords $AC$ and $BD$ .