Question

The length of a tangent from a point $A$ at distance $5$ cm from the centre of the circle is $4$ cm. Find the radius of the circle.

Answer 1

Given: $OA=5$ cm and $AB=4$ cm

$\Delta AOB$ is right angle triangle, right angle at $B$

By using Pythagoras Theorem, we have

$O{B}^2+A{B}^2=O{A}^2$

$OB$ is the radius of triangle

$O{B}^2+16=25$

$⟹O{B}^2=25-16$

$⟹O{B}^2=9$

$⟹OB=\sqrt{9}=3cm$

Radius of circle is $3$ cm