MathDB

MEMO 2010, Problem I-3: Three lines meet at one point

Source:

September 11, 2010

geometrycircumcirclecyclic quadrilateralradical axisgeometry proposedAngle Chasing

Problem Statement

We are given a cyclic quadrilateral

ABCD

with a point

E

on the diagonal

AC

such that

AD=AE

and

CB=CE

. Let

M

be the center of the circumcircle

k

of the triangle

BDE

. The circle

k

intersects the line

AC

in the points

E

and

F

. Prove that the lines

FM

AD

and

BC

meet at one point.
(4th Middle European Mathematical Olympiad, Individual Competition, Problem 3)