Q. 74.4( 20 Votes )

# In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the ∠RQS.

Given : Tangents PQ and PR are drawn to a circle such that RPQ = 30°. A chord RS is drawn parallel to the tangent PQ.

To Find : RQS

PQ = PR [Tangents drawn from an external point to a circle are equal]

PRQ = PQR [Angles opposite to equal sides are equal] [1]

In PQR

PRQ + PQR + QPR = 180°

PQR + PQR + QPR = 180° [Using 1]

2PQR + RPQ = 180°

2PQR + 30 = 180

2PQR = 150

PQR = 75°

QRS = PQR = 75° [Alternate interior angles]

QSR = PQR = 75° [angle between tangent and the chord equals angle made by the chord in alternate segment]

Now In RQS

RQS + QRS + QSR = 180

RQS + 75 + 75 = 180

RQS = 30°

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