If G is the centroid of a `DeltaABC`, then `GA^(2)+GB^(2)+GC^(2)` is equal to

Options

A. `a^(2)+b^(2)+c^(2)`
B. `(a^(2)+b^(2)+c^(2))/3`
C. `(a^(2)+b^(2)+c^(2))/2`
D. `((a+b+c)^(2))/3`

Explanation

To solve the problem, we need to find the value of \( GA^2 + GB^2 + GC^2 \) where \( G \) is the centroid of triangle \( ABC \).

### Step-by-Step Solution:

1. **Understanding the Centroid**:
The centroid \( G \) of a triangle \( ABC \) is the point where the three medians intersect. It divides each median in the ratio \( 2:1 \).

2. **Using the Median Formula**:
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