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 \( r \), chords of lengths \( a \) and \( b \) subtend angles \( \theta \) and \( 3\theta \) respectively at the center. We will derive the relationship \( r = a \sqrt{\frac{a}{3a - b}} \).

### Step 1: Use the Cosine Rule in Triangle OAB
In triangle OAB, where O is the center of the circle, we can apply the cosine rule. The cosine rule states that for any triangle with sides \( a, b, c \) opposite to angles \( A, B, C \) respectively:

\[ c^2 = a^2 + b^2 - 2ab \cos(C) \]
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