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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