MathDB

The circumcentre

O

of a given cyclic quadrilateral

ABCD

lies inside the quadrilateral but not on the diagonal

AC

. The diagonals of the quadrilateral intersect at

I

. The circumcircle of the triangle

AOI

meets the sides

AD

and

AB

at points

P

and

Q

, respectively; the circumcircle of the triangle

COI

meets the sides

CB

and

CD

at points

R

and

S

, respectively. Prove that

PQRS

is a parallelogram.

Problem Statement