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 at M and N, respectively. The line perpendicular to AB at M intersects l at D, and the line perpendicular to AC at N intersects l at F. Show that the point of intersection of the angle bisectors of angles MDA and NFA belongs to the line KE. geometryJuniorBalkanshortlistconcurrent