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# In the Given Figure, Pq is the Diameter of the Circle Whose Centre is O. Given ∠Ros = 42°, Calculate ∠Rts. - ICSE Class 10 - Mathematics

ConceptArc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle

#### 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°= 21°
∴ In right triangle PST,
∠PTS = 90° -∠SPT
⇒ ∠RTS = 90°- 21° = 69°

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Solution In the Given Figure, Pq is the Diameter of the Circle Whose Centre is O. Given ∠Ros = 42°, Calculate ∠Rts. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.
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