#### 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.