MathDB

Given a convex quadrilateral

ABCD

with

AB = BC

and

\angle ABD = \angle BCD = 90

.Let point

E

be the intersection of diagonals

AC

and

BD

. Point

F

lies on the side

AD

such that

\frac{AF}{F D}=\frac{CE}{EA}

.. Circle

\omega

with diameter

DF

and the circumcircle of triangle

ABF

intersect for the second time at point

K

. Point

L

is the second intersection of

EF

and

\omega

. Prove that the line

KL

passes through the midpoint of

CE

. Proposed by Mahdi Etesamifard and Amir Parsa Hosseini - Iran

Problem Statement