In the given figure, PQ is the diameter of the circle whose centre is O. Given ∠ROS = 42°, Calculate ∠RTS.
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°
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.