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Parallelity and equal angles given, wanted an angle equality

Source: 2022 Turkey JBMO TST P4

March 15, 2022
geometryParallel LinesAngle condition

Problem Statement

Given a convex quadrilateral ABCDABCD such that m(ABC^)=m(BCD^)m(\widehat{ABC})=m(\widehat{BCD}). The lines ADAD and BCBC intersect at a point PP and the line passing through PP which is parallel to ABAB, intersects BDBD at TT. Prove that m(ACB^)=m(PCT^)m(\widehat{ACB})=m(\widehat{PCT})
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