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Question
In the given figure, PQ is the diameter of the circle whose centre is O. Given ∠ROS = 42°, calculate ∠RTS.
Solution
Join PS.
∠PSQ = 90°
(Angle in a semicircle)
Also, `∠SPR=1/2 ∠ROS`
(Angle ate the centre is double the angle at the circumference subtended by the same chord)
`=> SPT =1/2 xx 42^circ = 21^circ`
∴ In right triangle PST,
∠PTS = 90° – ∠SPT
`=>` ∠RTS = 90° – 21° = 69°
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