MathDB

In a quadrilateral

ABCD,

AB=BC=DA/\sqrt{2},

and

\angle ABC

is a right angle. The midpoint of

BC

E,

the orthogonal projection of

C

AD

F,

and the orthogonal projection of

B

CD

G.

The second intersection point of circle

(BCF)

(with center

H

) and line

BG

K,

and the second intersection point of circle

(BCF)

and line

HK

L.

The intersection of lines

BL

and

CF

M.

The center of the Feurbach circle of triangle

BFM

N.

Prove that

\angle BNE

is a right angle.
Proposed by Zsombor Fehér, Cambridge

Problem Statement