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 ⊥ PT
In the right Δ OTP,we have:

`OP^2 = OT^2 +TP^2 `   [By Pythagoras’ theorem:]

`OT^2 =  sqrt(OP^2 - TP^2 )`

    `=sqrt(25^2 - 24^2`

    `= sqrt(625-576)`

    `=sqrt(49)`

     = 7 cm

∴ The length of the radius is 7cm.