MathDB

Given is an equilateral triangle

ABC

and an arbitrary point, denoted by

E

, on the line segment

BC

. Let

l

be the line through

A

parallel to

BC

and let

K

be the point on

l

such that

KE

is perpendicular to

BC

. The circle with centre

K

and radius

KE

intersects the sides

AB

and

AC

M

and

N

, respectively. The line perpendicular to

AB

M

intersects

l

D

, and the line perpendicular to

AC

N

intersects

l

F

. Show that the point of intersection of the angle bisectors of angles

MDA

and

NFA

belongs to the line

KE

Problem Statement