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A circle centred at 'O' has radius 1 and...

A circle centred at 'O' has radius 1 and contains the point A. Segment AB is tangent to the circle at A and `angleAOB =theta`. If point C lies on OA and BC bisects the angle ABO then OC equals

Text Solution

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`/_\ABO` is a right angle triangle
`(AB)/(OA)=tantheta`
`AB=tantheta`
`OB=sectheta`
By angle bisector theoram
`(OB)/(OC)=(BA)/(AC)`
`sectheta/(OC)=tantheta/(AC)`
`ACsectheta=OCtantheta`
...
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