Q. 94.2( 28 Votes )

In figure 3.89, line l touches the circle with centre O at point P. Q is the mid point of radius OP. RS is a chord through Q such that chords RS || line l. If RS = 12 find the radius of the circle.



Answer :

The radius of the circle will bisect the chord RS. Therefore, RQ = QS = 1/2 × 12 = 6


Let the radius of circle be r,


Now, in Δ OQS, we have,


RQ = 6


OR = r


OQ = 1/2 r


Applying Pythagoras theorem, we get,





3r2 = 4 × 36


r2 = 4 × 12 = 48


r = √48 units


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