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PQ forms equal angles with AB and CD

Source: IberoAmerican 1987 Q6

November 12, 2010
geometrycircumcirclesymmetryangle bisectorgeometry proposed

Problem Statement

Let ABCDABCD be a convex quadrilateral and let PP and QQ be the points on the sides ADAD and BCBC respectively such that APPD=BQQC=ABCD\frac{AP}{PD}=\frac{BQ}{QC}=\frac{AB}{CD}. Prove that the line PQPQ forms equal angles with the lines ABAB and CDCD.
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