Question 139
A convex quadrilateral $ABCD$ is given. It appears that on diagonal $AC$ there exists a point that lies on perpendicular bisectors of the segments $AB$ and $CD$, and on diagonal $BD$ there exists a point that lies on perpendicular bisectors of the segments $DA$ and $BC$.
Prove that $ABCD$ is a rectangle. (N. Agakhanov)
Prove that $ABCD$ is a rectangle. (N. Agakhanov)