MathDB
Concurrency problem

Source: Romania 2017 IMO TST 1, problem 1

March 18, 2018
geometrytrapezoidcircumcirclemoving pointsconicromaniaprojective geometry

Problem Statement

Let ABCDABCD be a trapezium, AD∥BCAD\parallel BC, and let E,FE,F be points on the sidesABAB and CDCD, respectively. The circumcircle of AEFAEF meets ADAD again at A1A_1, and the circumcircle of CEFCEF meets BCBC again at C1C_1. Prove that A1C1,BD,EFA_1C_1,BD,EF are concurrent.
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