# Is it long?

Geometry Level 5

Consider $$\triangle ABC$$ having sides $$AB=AC=14 \text{ cm}$$ and $$BC=20 \text{ cm}$$.

Let $$I$$ be the incentre of $$\triangle ABC$$ and $$G$$ be the centroid of the triangle formed by joining the points at which the sides $$AB,BC$$ and $$CA$$ are tangent to the incircle of $$\triangle ABC$$.

If $$IG=\dfrac{a\sqrt{b}}{c}\text{ cm}$$ where $$\gcd (a,c)=1$$ and $$b$$ is square-free, then submit your answer as $$a+b+c$$.

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