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 triangle with sides in geometric progression (G.P.) and the relationship between the angles. Let's denote the sides of the triangle as follows:

1. Let the smallest side be \( a \).
2. The second side will be \( ar \) (where \( r \) is the common ratio).
3. The largest side will be \( ar^2 \).

Given that the largest angle is twice the smallest angle, we can denote the angles opposite these sides as follows:

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