MathDB

Let all vertices of a convex quadrilateral

ABCD

lie on the circumference of a circle with center

O

. Let

F

be the second intersection point of the circumcircles of the triangles

ABO

and

CDO

. Prove that the circle passing through the points

A, F

and

D

also passes through the intersection point of the segments

AC

and

BD

.
(A Zaslavskiy)

Problem Statement