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Triangle ABCABCABC with its centroid at GGG has side lengths AB=15,BC=18,AC=25AB=15, BC=18,AC=25AB=15,BC=18,AC=25. DDD is the midpoint of BCBCBC.
The length of GDGDGD can be expressed as adb \frac{ a \sqrt{d} } { b} bad, where aaa and bbb are coprime positive integers and ddd is a square-free positive integer.
Find a+b+d+1 a + b + d + 1 a+b+d+1.
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