Given line *l *is a tangent.

Let the radius of circle be r.

OP is the radius.

OP line *l.* [Tangent theorem]

Given chord RSline *l*.

OP chord RS

Since the perpendicular from centre of the circle to the chord bisects the chord,

QS = ½ RS

QS = ½ ×12 = 6

OQ = r/2 [Given Q is the midpoint of OP]

In OQS

OS^{2} = OQ^{2}+QS^{2 }[Pythagoras theorem]

r^{2} = (r/2)^{2}+6^{2}

r^{2}-r^{2}/4 = 36

(3/4)r^{2} = 36

r^{2} = 36×4/3

r^{2}= 48

r = 4√3

Hence radius of circle is 4√3cm.