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2018 IMO Problems/Problem 6

Revision as of 23:44, 10 July 2018 by Btc433 (talk | contribs) (Created page with "A convex quadrilateral <math>ABCD</math> satisfies <math>AB\cdot CD=BC \cdot DA.</math> Point <math>X</math> lies inside <math>ABCD</math> so that <math>\angle XAB = \angle XC...")
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A convex quadrilateral $ABCD$ satisfies $AB\cdot CD=BC \cdot DA.$ Point $X$ lies inside $ABCD$ so that $\angle XAB = \angle XCD$ and $\angle XBC = \angle XDA.$ Prove that $\angle BXA + \angle DXC = 180^{\circ}$ .

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