In any triangle `A B C ,(a^2+b^2+c^2)/(R^2)` has the maximum value of 3 (b) 6 (c) 9 (d) none of these

Explanation

To solve the problem of finding the maximum value of \(\frac{a^2 + b^2 + c^2}{R^2}\) in any triangle \(ABC\), we can follow these steps:

### Step 1: Use the Sine Rule
According to the sine rule, we have:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R \]
From this, we can express \(a\), \(b\), and \(c\) in terms of \(R\) and the sine of the angles:
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