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SAMO Problem 2: Determine ratio in a triangle

Source: South African Mathematics Olympiad 2018, Problem 2

July 27, 2018
ratiogeometry

Problem Statement

In a triangle ABCABC, AB=ACAB = AC, and DD is on BCBC. A point EE is chosen on ACAC, and a point FF is chosen on ABAB, such that DE=DCDE = DC and DF=DBDF = DB. It is given that DCBD=2\frac{DC}{BD} = 2 and AFAE=5\frac{AF}{AE} = 5. Determine that value of ABBC\frac{AB}{BC}.
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