MathDB

Let

ABCD

be a cyclic quadrilateral whose diagonals

AC

and

BD

are perpendicular. Let

O

be the circumcenter of

ABCD

K

the intersection of the diagonals,

L\neq O

the intersection of the circles circumscribed to

OAC

and

OBD

, and

G

the intersection of the diagonals of the quadrilateral whose vertices are the midpoints of the sides of

ABCD

. Prove that

O, K, L

and

G

are collinear

Problem Statement