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Trapezoid And Segment

Source: Iranian RMM TST Day2 P4

January 14, 2020
geometrymoving points

Problem Statement

In a trapezoid ABCDABCD with ADAD parallel to BCBC points E,FE, F are on sides AB,CDAB, CD respectively. A1,C1A_1, C_1 are on AD,BCAD,BC such that A1,E,F,AA_1, E, F, A lie on a circle and so do C1,E,F,CC_1, E, F, C. Prove that lines A1C1,BD,EFA_1C_1, BD, EF are concurrent.
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