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MCQ

Fill in the Blanks

In the following figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to ______

#### Options

100°

80°

90°

75°

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#### Solution

In the following figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to **100°**.

**Explanation:**

From figure using properties of circle and tangents

∠OPQ = 90° - 50°

∠OPQ = 40°

OP = OQ = radius

So (∠E) = ∠OQP = 40°

Now In ∆POQ

∠POQ = 180° – (∠OPQ + ∠OQP)

∠POQ = 180° – (40° + 40°)

∠POQ = 100°

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

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