Question

Tangents PQ and PR are drawn from an external point P to a circle with centre O, such that angle RPQ=30°. A chord RS is drawn parallel to the tangent PQ. Find angle RQS.

Answer is 30° but solve karke btao jaldi please....

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Answer 1

Answer:

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30°

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It is given that, ∠RPQ=30°

and PR and PQ are tangents drawn from P to the same circle.Hence PR=PQ [Since tangents drawn from an external point to a circle are equal in length]∴ ∠PRQ=∠PQR [Angles opposite to equal sides are equal in a triangle. ]In △PQR,∠RQP+∠QRP+∠RPQ=180°

[Angle sum property of a triangle ]

[Angle sum property of a triangle ]⇒ 2∠RQP+30°=180°

⇒ 2∠RQP=150°

⇒ ∠RQP=75°

so ∠RQP=∠QRP=75°

⇒ ∠RQP=∠RSQ=75 [ By Alternate Segment Theorem]Given, RS∥PQ∴ ∠RQP=∠SRQ=75°

[Alternate angles]⇒ ∠RSQ=∠SRQ=75°

∴ QRS is also an isosceles triangle. [Since sides opposite to equal angles of a triangle are equal.]⇒ ∠RSQ+∠SRQ+∠RQS=180°

[Angle sum property of a triangle]⇒ 75°+75°+∠RQS=180°

⇒ 150°+∠RQS=180°

∴ ∠RQS=30°

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I hope this helps you.........

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