In a non isoceles triangle ABC, let the perpendicular bisector of [BC] intersect (ABC) at M and N respectively. Let the midpoints of [AM] and [AN] be K and L respectively. Let (ABK) and (ABL) intersect AC again at D and E respectively, let (ACK) and (ACL) intersect AB again at F and G respectively.
Prove that the lines DF, EG and MN are concurrent. Turkeygeometryperpendicular bisectormenelaus theorem