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PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°, then ∠OPQ is

  • a)
    60°

  • b)
    45°

  • c)
    30°

  • d)
    90°

Correct answer is option 'C'. Can you explain this answer?
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PQ is a tangent drawn from a point P to a circle with centre O and QOR...
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PQ is a tangent drawn from a point P to a circle with centre O and QOR...

Given- PQ is a tangent to a circle with centre O at Q. QOR is a diameter of the given circle so that ∠POR=120o. To find out- ∠OPQ=?
Solution- QOR is a diameter.
∴OQ is a radius through the point of contact Q of the tangent PQ. ∴∠OQP=90o since the radius through the point  of contact of a tangent to a circle is perpendicular  to the tangent.∴∠OPQ+∠OQP=120o
(external angles of a triangle=sum of the internal opposite angles )
∴∠OPQ = 120− 90= 30o.
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PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°, then ∠OPQ isa)60°b)45°c)30°d)90°Correct answer is option 'C'. Can you explain this answer?
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