Question

In the given figure, seg RS is a diameter of the circle with centre O. Point T lies in the exterior of the circle. Prove that ∠ RTS is an acute angle.

Answer 1

Join RT and TS. Suppose RT intersect the circle at P.



It is given that seg RS is a diameter of the circle with centre O.

∴ ∠RPS = 90º (Angle in a semi-circle is 90º)

In ∆PTS, ∠RPS is an exterior angle and ∠PTS is its remote interior angle.

We know, an exterior angle of a triangle is greater than its remote interior angle.

∴ ∠RPS > ∠PTS

⇒ 90º > ∠PTS

Or ∠RTS < 90º (∠PTS = ∠RTS)

Thus, ∠RTS is an acute angle.