# Right within Equilateral

Geometry Level 3

In $$\triangle ABC$$, $$AB= \dfrac{\sqrt{3}}{2}$$, $$BC=1$$ and $$\angle B = 90^{\circ}$$. $$PQR$$ is an equilateral triangle with sides $$PQ$$, $$QR$$ and $$RP$$ passing through the points $$A$$, $$B$$ an $$C$$ respectively and each having length $$2$$.

If the sum of the possible lengths of the segment $$BR$$ be expressed as $$\dfrac{a}{b}$$, where $$a$$ , $$b$$ are coprime positive integers, find the value of $$a+b$$

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