Triangle trials

Geometry Level 2

Triangle ABCABC with its centroid at GG has side lengths AB=15,BC=18,AC=25AB=15, BC=18,AC=25. DD is the midpoint of BCBC.

The length of GDGD can be expressed as adb \frac{ a \sqrt{d} } { b} , where aa and bb are coprime positive integers and dd is a square-free positive integer.

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

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