In the adjoining figure, A, B, and C are three points on a circle O. If angle AOB = 90° and angle BOC = 120°, then angle ABC is:

60°

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75°

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60°

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30°

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Solution

The correct option is B
75°

angle AOC = 360° - (angle AOB + angle BOC)

angle AOC = 360° - 90° + 120° = 150°

therefore angle ABC = 1/2 × angle AOC = 75°

[because, The angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any other point on the remaining part of the circle]

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Similar questions

In figure, A, B and C are three points on a circle with centre O such that $∠$ BOC = $30^{\circ}$ and $∠$ AOB = $60^{\circ}$ . If D is a point on the circle other than the arc ABC, find $∠$ ADC.

Q. If A , B, C are three points on a circle with centre O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =

(a) 60°

(b) 75°

(c) 90°

(d) 135°

Q. In the given figure, A, B and C are three points on the circle with centre O such that

∠ B O C = 30^{\circ}

and

∠ A O B = 60^{\circ}

. If D is a point on the circle that is not on the arc ABC, then find

∠ A B C .

Q. In the figure

A, B

and

C

are three points on a circle with centre

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such that

∠ B O C = 30^{o}

and

∠ A O B = 60^{o}

. If

D

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∠ A D C

In the adjoining figure. A, B, C are three points on a circle O. If $∠$ AOB = 90 $^{\circ}$ and $∠$ BOC = 120 $^{\circ}$ , then $∠$ ABC in degree is -

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