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In the given figure, O is the centre of ...

In the given figure, `O` is the centre of a circle and`/_ AOC = 130^(@)` . Then , `/_ ABC = ?`

A

`50^(@)`

B

`65^(@)`

C

`115^(@)`

D

`130^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Take a point `D` on the remaining part of the circumference.
Join `AD` and `CD.` Then,
`/_ ADC = (1)/(2) /_ AOC = (1)/(2) xx 130^(@) = 65^(@)`
In cyclic quadrilateral ABCD, we have
`/_ ABC +/_ADC = 180^(@) implies /_ ABC + 65^(@) = 180^(@)`
` /_ ABC= 180^(@) -65^(@) =115^(@)`
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RS AGGARWAL-CIRCLES -MULTIPLE CHOICE QUESTION(MCQ)
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  5. In the given figure, AOB is a diameter and ABCD is a cyclic quadrilate...

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  6. In the given figure, ABCD is a cyclic quadrilateral in which AB || DC ...

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  7. In the given figure, O is the centre of a circle and/ AOC = 130^(@) . ...

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  8. In the given figure, AOB is a diameter of a circle and CD||AB . If / ...

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  9. In the given figure, O is the centre of a circle in which /AOC =100^(@...

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  10. In the given figure, O is the centre of a circle and / OAB = 50^(@). T...

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  12. In the given , equilateral DeltaABC is inscribed in a circle and ABDC ...

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  13. In the given figure, sides AB and AD of quad. ABCD are produced to E a...

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  14. In the given figure, , O is the centre of a circle and / AOB = 140^(@)...

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  15. In the given figure , Ois the centre of a circle and / AOB = 130^(@). ...

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  16. In the given figure, ABCD and ABEF aretwo cyclic quadrilaterals. If / ...

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  17. In the given figure, ABCD is a cyclic quadrilateral in which DC is pro...

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  18. Two chords AB and CD of a circle intersect each other at a point E out...

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  19. In the given figure , A and B are the centres of two circles having ra...

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  20. In the given figure, / AOB = 90^(@) and / ABC = 30^(@) . Then / CAO = ...

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