Three parallel chords of a circle have lengths 2,3,4 units and subtend angles `alpha,beta,alpha+beta` at the centre, respectively `(alphaltbetaltpi),` then find the value of `cosalpha`

Explanation

We can draw the diagram with the given details.

Please refer to video to see the diagram.

Now, from the diagram,

`B = alpha/2`

`:.` Using cosine rule,

`:. cos (alpha/2) = (3^2+4^2-2^2)/(2*3*4)`

` cos (alpha/2) = 21/24 = 7/8`

`:. cos alpha =2cos^2(alpha/2) -1 = 2(7/8)^2 -1`

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