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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

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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°

  Is there an error in this question or solution?
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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