MathDB

Given a quadrilateral

ABCD

simultaneously inscribed and circumscribed, assume that none of its diagonals or sides is a diameter of the circumscribed circle. Let

P

be the intersection point of the external bisectors of the angles near

A

and

B

. Similarly, let

Q

be the intersection point of the external bisectors of the angles

C

and

D

. If

J

and

O

respectively are the incenter and circumcenter of

ABCD

prove that

OJ\perp PQ

Problem Statement