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Question

# O is the centre of the circle as shown in the figure, ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm. 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 line segment PQ passes through the centre O, so PQ is the diameter of the circle. PQ=4 cm=2×OQ=2× radius, On joining RQ. ∠PRQ=90∘ [∵ Angle subtended by diameter on the circle is 90∘] ∴∠ORQ=90∘−35∘=55∘ But, OR=OQ ∴∠ORQ=∠OQR=55∘ ∴y=180∘−(55∘+55∘)=70∘ [Sum of angles of a triangle is 180∘]

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