NL-NWO 1995 Problem 2

For any point $P$ on a segment $AB$ , isosceles and right-angled triangles $AQP$ and $PRB$ are constructed on the same side of $AB$ , with $AP$ and $PB$ as the bases. Determine the locus of the midpoint $M$ of $QR$ when $P$ describes the segment $AB$ .