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line connecting midpoints BE,AD divide diagonals AC,BC in the same ratio

Source: 2004 Oral Moscow Geometry Olympiad grade 10 p1

October 28, 2020
geometryratiomidpoints

Problem Statement

EE and FF are the midpoints of the sides BCBC and ADAD of the convex quadrilateral ABCDABCD. Prove that the segment EFEF divides the diagonals ACAC and BDBD in the same ratio.
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