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computational from New Zealand, segments (2019 NZMO 1.3 )

Source:

January 10, 2021
geometry

Problem Statement

In triangle ABCABC, points DD and EE lie on the interior of segments ABAB and ACAC, respectively,such that AD=1AD = 1, DB=2DB = 2, BC=4BC = 4, CE=2CE = 2 and EA=3EA = 3. Let DEDE intersect BCBC at FF. Determine the length of CFCF.
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