MathDB

G1

Part of 2017 Romanian Master of Mathematics Shortlist

Problems(1)

Concurrency problem

Source: Romania 2017 IMO TST 1, problem 1

3/18/2018
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.
geometrytrapezoidcircumcirclemoving pointsconicromaniaprojective geometry