Question

In 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

Answer :

angle RTS is an acute angle

Step by step explanation :

constuction:-

Draw seg RT and RS

Take point P on the circle on line RT

Draw seg PS

Proof :-

In triangle RPS,

angle RPS =90° -(1) (angle inscribed in semicircle is right angle)

In triangle PST,

angle RPS is an exterior angle of triangle PST

angle RPS > angle PTS (Exterior angle theorem)

i.e. angle PTS < angle RPS

angle PTS < 90° [from (1)]

angle RTS < 90° (R-P-T)

i.e. angle RTS is an acute angle

Hence Proved