MathDB

Let

ABCD

be a cyclic quadrilateral. Let lines

AB

and

CD

intersect in

P,

and lines

BC

and

DA

intersect in

Q.

The feet of the perpendiculars from

P

BC

and

DA

are

K

and

L,

and the feet of the perpendiculars from

Q

AB

and

CD

are

M

and

N.

The midpoint of diagonal

AC

F.

Prove that the circumcircles of triangles

FKN

and

FLM,

and the line

PQ

are concurrent.
Based on a problem by Ádám Péter Balogh, Szeged

Problem Statement