Question

B R S are two points on a circle,

Centre O.
TS is a tangent to the circle.
Angle RST = x
Prove that ROS=2X
You must give reasons for each stage
of your working​

Answer 1

Proved!

Explanation:

Since TS is a tangent to the circle, ∠TSO = 90°.

Hence, ∠OSR = 90° - x.

Since OS and OR are radius, OS = OR.

So, ∠ORS = ∠OSR = 90° - x.

Thus, ∠ROS = 180° - ∠OSR - ∠ORS = 180° - 2 * (90° - x) = 180° - 180° + 2x = 2x.

So, it is proved.