Question

Tangents PQ and PR are drawn from 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 RQS

Answer 1

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Answer 2

ANSWER..

Given, RS ∥ PQ and ∠RPQ = 30°

PR = PQ (equal tangents)

∠PRQ = ∠PQR (angle opposite to equal sides)

In △PQR,

∠PRQ + ∠PQR + ∠RQP = 180°

2∠PQR + 30° = 180°

∠PQR = 75°

∠SRQ = ∠PQR = 75° (alternate angle)

Also, ∠RQP = ∠RSQ = 75°

(alternate segment angles)

∠RSQ = ∠SRQ = 75°

In △QSR,

∠RSQ + ∠SRQ + ∠SQR = 180°

75° + 75° + ∠SQR = 180°

∠SQR=30°

∠SQR=30°∠RQS=30°

hope it helps u..