Question

4. In figure 3.58, seg RS is a diameter of the
circle with centre 0. Point T lies in
the exterior of the circle. Prove that
Z RTS is an acute angle.​

Answer 1

Step-by-step explanation:

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 acutme angle

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