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Question

In the given figure, O is the centre of a circle and PQ is a diameter. If ROS=40, then what is the value of RTS?

A
20
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B
45
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C
70
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D
65
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Solution

The correct option is C 70
Since PQ is the diameter, we have
PRQ=90 [angle in a semi circle]
But, PRQ+TRQ=180. [linear pair of angles]
90+TRQ=180TRQ=90

Since the angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any remaining point on the circle, we have
ROS=2RQS
i.e., 40=2RQS
RQS=402=20

Using angle sum property in RQT, we have
RQT+QTR+TRQ=180.
i.e., 20+RTS+90=180
RTS=180110=70

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