Question

A tangent at a point $A$ on the circle meets a line through the centre of the circle at a point $B$ so that $OB=13cm$ and $AB=12cm$. Find the radius of the circle.

• A. $3cm$
• B. $5cm$
• C. $7cm$
• D. $10cm$

Answer 1

The correct option is B

$5cm$

Since, tangent at a point is perpendicular to the radius through that point,

$OA\perp AB$

In $△OAB$, applying Pythagoras Theorem,

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

$\Rightarrow {13}^2=O{A}^2+{12}^2$

$\Rightarrow O{A}^2={13}^2-{12}^2$

$\Rightarrow O{A}^2=169-144=25$

$\Rightarrow OA=\sqrt{25}=5cm$

Hence, radius of the circle is $5cm$