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A,B and C are three points on a circle s...

A,B and C are three points on a circle such that the angles subtended by the chords AB and AC at the centre O are `90^@` and `110^@` respectively . Further suppose that the centre O lies on the interior `angleBAC`. The `angle BAC` is

A

`20^(@)`

B

`40^(@)`

C

`80^(@)`

D

`160^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C

`Delta AOB` में,
`angle AOB =90^(@)`
`because OA = OB =r`
`therefore angle OAB = angle OBA = (180^(@)-90^(@))/(2)=45^(@)`
`Delta AOC` में
`OA =OC`
`therefore angle OAC = angle OCA =(180^(@)-110^(@))/(2) =35^(@)`
`therefore angle BAC = angle OAB + angle OAC = 45^(@) +35^(@) =80^(@)`
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