Question

A point P is 25 cm away from the center of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.

Answer 1

Draw a circle and let p be a point such that OP = 25cm.

Let TP be the tangent, so that TP = 24cm

join OT where OT is radius.

Now, tangent drawn from an external point is perpendicular to the radius at the point of contact.

∴ OT \(\perp\) PT

In the right \(\triangle OTP,\) we have:

∴ The length of the radius is 7cm.