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Home » If PQ is a tangent to the circle at R; calculate: i) ∠PRS ii) ∠ROT When O is the centre of the circle and ∠TRQ = 30degree
If PQ is a tangent to the circle at R; calculate: i) ∠PRS ii) ∠ROT When O is the centre of the circle and ∠TRQ = 30degree
Class 10 | Exercise 18B | ICSE | Maths | Selina | Tangents and Intersecting Chords
If PQ is a tangent to the circle at R; calculate: i) ∠PRS ii) ∠ROT When O is the centre of the circle and ∠TRQ = 30degree

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(B) - 6

Solution:

(i) As

    \[PQ\]

is the tangent and

    \[OR\]

is the radius.

So,

    \[OR\bot PQ\]

    \[\angle ORT\text{ }=\text{ }{{90}^{o}}\]

    \[\angle TRQ\text{ }=\text{ }{{90}^{o}}-\text{ }{{30}^{o}}~=\text{ }{{60}^{o}}\]

But in

    \[\vartriangle OTR\]

we have

    \[OT\text{ }=\text{ }OR\]

[Radii of same circle]

    \[\angle OTR\text{ }=\text{ }{{60}^{o}}~or\angle STR\text{ }=\text{ }{{60}^{o}}\]

But,

    \[\angle PRS\text{ }=\angle STR\text{ }=\text{ }{{60}^{o}}\]

 [Angles in the alternate segment]

(ii) In

    \[\vartriangle OTR\]

    \[\angle ORT\text{ }=\text{ }{{60}^{o}}~\]

    \[\angle OTR\text{ }=\text{ }{{60}^{o}}\]

Thus,

    \[\angle ROT\text{ }=\text{ }{{180}^{o}}-\text{ }({{60}^{o}}~+\text{ }{{60}^{o}})\]

So,

    \[=\text{ }{{180}^{o}}-\text{ }{{120}^{o}}~=\text{ }{{60}^{o}}\]

i

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