MathDB

There exists point

O

inside a convex quadrilateral

ABCD

satisfying

OA=OB

and

OC=OD

, and

\angle AOB = \angle COD=90^{\circ}

. Consider two squares, (1)square having

AC

as one side and located in the opposite side of

B

and (2)square having

BD

as one side and located in the opposite side of

E

. If the common part of these two squares is also a square, prove that

ABCD

is an inscribed quadrilateral.

Problem Statement