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Let ABCD be a convex quadrilateral. A circle passing through the points A and D and a circle passing through the points B and C are externally tangent at a point P inside the quadrilateral. Suppose that \angle{PAB}+\angle{PDC}\leq  90^\circ and \angle{PBA}+\angle{PCD}\leq  90^\circ.
Prove that AB+CD \geq  BC+AD.

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