Problem

Source:

Tags: geometry



For an arbitrary point $P$ on a given segment $AB$, two isosceles right triangles $APQ$ and $PBR$ with the right angles at $Q$ and $R$ are constructed on the same side of the line $AB$. Prove that the distance from the midpoint $M$ of $QR$ to the line $AB$ does not depend on the choice of $P$.