MathDB
geom problem

Source: PMO

March 19, 2021
geometryPMO

Problem Statement

In convex quadrilateral ABCDABCD, ∠CAB=∠BCD\angle CAB = \angle BCD. PP lies on line BCBC such that AP=PCAP = PC, QQ lies on line APAP such that ACAC and DQDQ are parallel, RR is the point of intersection of lines ABAB and CDCD, and SS is the point of intersection of lines ACAC and QRQR. Line ADAD meets the circumcircle of AQSAQS again at TT. Prove that ABAB and QTQT are parallel.
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