In a convex quadrilateral ABCD we draw the bisectors ℓa, ℓb, ℓc, ℓd of external angles A, B, C, D respectively. The intersection points of the lines ℓa and ℓb, ℓb and ℓc, ℓc and ℓd, ℓd and ℓa are designated by K, L, M, N. It is known that 3 perpendiculars drawn from K on AB, from L om BC, from M on CD intersect at one point. Prove that the quadrilateral ABCD is cyclic. geometryangle bisectorConcyclic