n the adjoining figure, seg RS is a diameter of a circle with centre O. Point T lies in the exterior of the
circle. Prove that ∠RTS is an acute angle.
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Given: O is the centre of the circle, seg RS is the diameter of the circle. To prove: ∠RTS is an acute angle. Construction: Let seg RT intersect the circle at point P. Join PS and PT. Proof: seg RS is the diameter. [Given] ∴ ∠RPS = 90° [Angle inscribed in a semicircle] Now, ∠RPS is the exterior angle of ∆PTS. ∴ ∠RPS > ∠PTS [Exterior angle is greater than the remote interior angles] ∴ 90° > ∠PTS i.e. ∠PTS < 90° i.e, ∠RTS < 90° [R – P -T] ∠RTS is an acute angle.Read more on Sarthaks.com - https://www.sarthaks.com/851583/adjoining-figure-diameter-circle-with-centre-point-lies-exterior-circle-prove-that-rts
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