If the sides of a triangle are in G.P., and its largest angle is twice the smallest, then the common ratio `r` satisfies the inequality `0

Options

A. `0 lt r lt sqrt(2)`
B. `1 lt r lt sqrt(2)`
C. `1 lt r lt 2`
D. none of these

Explanation

To solve the problem, we need to analyze the conditions given about the triangle whose sides are in geometric progression (G.P.) and where the largest angle is twice the smallest angle.

### Step-by-step Solution:

1. **Define the sides of the triangle**:
Let the sides of the triangle be \( a/r, a, ar \), where \( a \) is a positive constant and \( r > 1 \) is the common ratio.

2. **Identify the angles**:
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