Prove that the external bisectors of the angles of a triangle meet the opposite sides in three collinear points.

I need to prove this using only Menelaus Theorem, Stewart's Theorem, Ceva's Theorem.

What I did:I tried by making a simple case diagram that is a diagram with obtuse angle in the given triangle. Then using Menelaus on angle bisectors with respect to the triangles and using angle bisector theorem for ratios of values.

I need to prove this using only Menelaus Theorem, Stewart's Theorem, Ceva's Theorem.

What I did:I tried by making a simple case diagram that is a diagram with obtuse angle in the given triangle. Then using Menelaus on angle bisectors with respect to the triangles and using angle bisector theorem for ratios of values.