MathDB

Let

ABC

be a triangle with

90^\circ \ne \angle A \ne 135^\circ

. Let

D

and

E

be external points to the triangle

ABC

such that

DAB

and

EAC

are isoscele triangles with right angles at

D

and

E

. Let

F = BE \cap CD

, and let

M

and

N

be the midpoints of

BC

and

DE

, respectively.
Prove that, if three of the points

A

F

M

N

are collinear, then all four are collinear.

Problem Statement