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Three parallel chords of a circle have l...

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

Text Solution

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From the given information we have the following diagram.
`AB = 4, AC = 2, BC = 3`
Using the geometry of the circle, we have `angle ABC = alpha//2`
Now in `Delta ABC`, using cosine rule

`cos (alpha//2) = ((3)^(2) + (4)^(2) - (2)^(2))/(2 xx (3) xx (4)) = (7)/(8)`
`rArr cos alpha = 2 cos^(2) (alpha//2) -1`
`= 2 xx (49)/(64) - 1 = (17)/(31)`
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