MathDB

Configuration with cyclic quadrilateral

Source: IMOC 2023 G3

September 9, 2023

geometrycyclic quadrilateral

Problem Statement

ABCD

is a cyclic quadrilateral with circumcenter

O

. The lines

AC, BD

intersect at

E

and

AD, BC

intersect at

F

.

O_1

and

O_2

are the circumcenters of

\triangle ABE

and

\triangle CDE

, respectively. Assume that

P, Q, F

and

(OO_1O_2)

intersect at two points

P, Q

. Prove that

P, Q, F

are collinear.

Back to Problems View on AoPS