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Possible Duplicate:
Prove that CX and CY are perpendicular

There is given convex quadrilateral ABCD. And internal bisectors of angle ∠A and ∠C intersect in point X. And internal bisectors of angle ∠B and ∠D intersect in point Y. Prove that if AY is is the external bisector of A then CY is the external bisector of C. enter image description here

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    I am closing as exact duplicate. Given the statement of the problem that $CY$ is the external bisector of $C$ is equivalent to $XCY$ being a right angle. ($XC$ is the internal bisector.)2012-12-07

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