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.

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