In a circle of radius `r ,` chords of length `aa n dbc m` subtend angles `thetaa n d3theta` , respectively, at the center. Show that `r=asqrt(a/(3a-b))c m`

Explanation

To solve the problem, we need to show that in a circle of radius \( r \), where chords of lengths \( a \) and \( b \) subtend angles \( \theta \) and \( 3\theta \) at the center, the relationship \( r = a \sqrt{\frac{a}{3a - b}} \) holds.

### Step-by-Step Solution:

1. **Identify the triangles**:
We have two triangles formed by the radius and the chords:
- Triangle \( OAB \) for chord \( AB \) with length \( a \) subtending angle \( \theta \).
- Triangle \( OBC \) for chord \( BC \) with length \( b \) subtending angle \( 3\theta \).
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