MathDB
AB=CD if PS// RQ, angle bisectors in trapezoid (2017 Kyiv City MO 8.4.1)

Source:

September 8, 2020
geometryangle bisectortrapezoidparallel

Problem Statement

In a trapezoid ABCDABCD with bases ADAD and BCBC, the bisector of the angle ∠DAB\angle DAB intersects the bisectors of the angles ∠ABC\angle ABC and ∠CDA\angle CDA at the points PP and SS, respectively, and the bisector of the angle ∠BCD\angle BCD intersects the bisectors of the angles ∠ABC\angle ABC and ∠CDA\angle CDA at the points QQ and RR, respectively. Prove that if PS∥RQPS\parallel RQ, then AB=CDAB = CD.
Back to ProblemsView on AoPS