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.

Answer :


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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