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Part of 2001 Cuba MO

Problems(1)

ellipse, tangents of 4 points 2001 Cuba MO 2.4

Source:

9/15/2024
The tangents at four different points of an arc of a circle less than 180o180^o intersect forming a convex quadrilateral ABCDABCD. Prove that two of the vertices belong to an ellipse whose foci to the other two vertices.
conicsellipseTangents