Question

PQ is a tangent drawn from an external point P to a circle with centre O and QOR is a diameter of the circle. If angle POR=120 degree then angle OPQ(in degree) is

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Answer 1

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GIVEN :-

● PQ is a tangent to a circle with centre O at Q. 

● QOR is a diameter of the given circle

● So that, ∠POR=120°

TO FIND :-

∠OPQ=?

SOLUTION :'

∠QOP + ∠POR = 180°

∠QOP + 120° = 180°

∠QOP = 180° - 120°

∠QOP = 60°

In ΔPOQ

∠QOP + ∠OPQ + ∠PQO = 180°

60° + ∠OPQ + 90° = 180°

150° + ∠OPQ = 180°

∠OPQ = 180° - 150°

∠OPQ = 30°