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.


Given line 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]
OS2 = OQ2+QS[Pythagoras theorem]
r2 = (r/2)2+62
r2-r2/4 = 36
(3/4)r2 = 36
r2 = 36×4/3
r2= 48
r = 4√3
Hence radius of circle is 4√3cm.

About Us

At AI Shiksha, we are driven by a singular mission – to democratize access to artificial intelligence education. We believe that AI is a transformative force that has the power to shape the future, and we are committed to making this cutting-edge technology accessible to everyone.