# 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 $$a+b$$.

Inspiration

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