A characteristic property of the ellipse.

Let (c) be a compact smooth convex curve in E² and A,B are interior points. The point M is on (c) and we denote e(M) the support line of the point M and e₀ the unit tangent vector at the point M. We suppose that: angle (AM,e₀)=angle(BM,-e₀).

Prove that (c) is an ellipse.