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Prove that the quadrilateral XA'BC' is cyclic (3)

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October 28, 2010
geometrycircumcirclegeometry proposed

Problem Statement

Points A′,B′,C′A', B', C' lie on sides BC,CA,ABBC, CA, AB of triangle ABC.ABC. for a point XX one has ∠AXB=∠A′C′B′+∠ACB\angle AXB =\angle A'C'B' + \angle ACB and ∠BXC=∠B′A′C′+∠BAC.\angle BXC = \angle B'A'C' +\angle BAC. Prove that the quadrilateral XA′BC′XA'BC' is cyclic.
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