# Triangle trials

Geometry Level 3

$$ABC$$ is a triangle with centroid $$G$$ and side lengths $$AB=15, BC=18,AC=25$$. $$D$$ is the midpoint of $$BC$$. The length of $$GD$$ can be expressed as $$\frac{ a \sqrt{d} } { b}$$, where $$a$$ and $$b$$ are coprime positive integers and $$d$$ is a square-free positive integer.

Find $$a + b + d + 1$$.

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