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PQ // AB wanted, equal arcs AF=BF, cyclic ABCD

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist G2 day2

September 30, 2021
parallelgeometrycongruent

Problem Statement

Let A,B,C,DA, B, C, D be points that lie on the same circle . Let FF be such that the arc AFAF is congruent with the arc BFBF. Let PP be the intersection point of the segments DFDF and ACAC. Let QQ be intersection point of the CFCF and BDBD segments. Prove that PQ∥ABPQ \parallel AB.
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