Question

PR and PS are two tangents drawn from an external point Pof the circle with centre at O. IfPR8
cm and <RPS - 60", then the length of RS is​

Answer 1

Step-by-step explanation:

Given : Tangents PR and PQ from an external point P to a circle with centre O.

To prove : Quadrilateral QORP is cyclic.

Proof : RO and RP are the radius and tangent respectively at contact point R.

∴∠PRO=90

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Similarly ∠PQO=90

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In quadrilateral OQPR, we have

∠P+∠R+∠O+∠Q=360

∘

⇒∠P+∠90

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+∠O+∠90

∘

=360

∘

⇒∠P+∠O=360

∘

−180

∘

=180

∘

These are opposite angles of quadrilateral QORP and are supplementary.

∴ Quadrilateral QORP is cyclic, hence, proved.