Extension extended

Geometry Level 4

\(\Delta\)ABC is an equilateral triangle with side length 1. AC, CB & AB are extended respectively to D, F & E such that E is a point on segment DF.

Given that, lengths: \[\text{CD} =10 \quad,\quad \text{BF}=1.\]

If the length of segment \(\color {Blue} {\text{BE}} \) can be expressed as \(\frac ab\) where \(a\) & \(b\) are coprime positive integers, then find \(a+b\).



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