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

Explanation

We can create a diagram with the given details.

Please refer to video for the diagram.

Now, in `Delta OAB`,

`cos theta = (r^2+r^2-a^2)/(2*r*r) = (2r^2-a^2)/(2r^2)`

`=>cos theta = 1-a^2/(2r^2)`

`=>a^2/(2r^2) = 1-costheta = 2sin^2(theta/2)`

`=>a =2rsin(theta/2)->(1)`

Now, in `Delta OCB`,

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