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Question

# O is the centre of the circle as shown in the figure. If ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm, then what is the measure of ∠ROQ ?

A
55
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B
35
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C
105
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D
70
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Solution

## The correct option is D 70∘ Since PQ is the diameter of circle, we have PQ=4 cm=2×OQ, where OQ is the radius of the circle. Join RQ. We know that the angle subtended by an arc of a circle at its centre is double the angle subtended by it on any remaining part of the circle. Since ∠POQ=180∘, we have ∠PRQ=180∘2=90∘. ∴∠ORQ=90∘−35∘=55∘ But , OR = OQ = radii of the circle. Since base angles of an isosceles triangle are equal, we have ∠ORQ=∠OQR=55∘. Using angle sum property, we have ∴y=180∘−(55∘+55∘)=70∘.

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