Multiple Choice Questions on In the given figure O is the centre of the circle If ang PRQ 40 deg then what is ang OPQ ........ for Mathematics - All Exams Preparation

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Multiple Choice Questions

In the given figure O is the centre of the circle If ang PRQ 40 deg then what is ang OPQ ........

Quantitative Aptitude ( CCS) Geometry
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    In the given figure, O is the centre of the circle. If ∠PRQ = 40°, then what is ∠OPQ?

    30°

    Incorrect Answer

    40°

    Incorrect Answer
    150°
    Incorrect Answer

    50°

    Correct Answer
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    Explanation:

    Given that, ∠PRQ = 40°, then what is ∠POQ = 80°

    (∴ The angle subtended by an arc at the centre is double the angle subtended by the same arc at a point on the remaining circle).
    In triangle OPQ, OP = OQ (radii)
    ∴ ∠OPQ = ∠OQP (? Angles opposite to equal sides) 
    ∠OPQ + ∠OQP + 80 = 180°
    ⇒ ∠OPQ = 50°

    By: Amit Kumar
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