Question

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

Answer 1

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°