Question

Find the radius of the circle if the length of the tangent is 16 cm and distance between center and external point is 20 cm.

Answer 1

We have,

OP = 20 cm & PT = 16 cm.

∵ OT \(\perp\) PT

(∵ Angle between radius and tangent at point of contact is 90°)

Now, in right △ OTP, we have

OP² = OT² + PT²

\(\Rightarrow\) OT² = OP² - PT² = 20² - 16²

\(\Rightarrow\) r² = 400 - 256

\(\Rightarrow\) r² = 144

\(\Rightarrow\) r = 12 cm

∵ Radius of the circle is 12 cm.