MathDB

International Zhautykov Olympiad 2011 - Problem 6

Source:

January 17, 2011

geometrycircumcirclesymmetryratiocyclic quadrilateralpower of a pointradical axis

Problem Statement

Diagonals of a cyclic quadrilateral

ABCD

intersect at point

K.

The midpoints of diagonals

AC

and

BD

are

M

and

N,

respectively. The circumscribed circles

ADM

and

BCM

intersect at points

M

and

L.

Prove that the points

K ,L ,M,

and

N

lie on a circle. (all points are supposed to be different.)