Question

A tangent $AB$ at a point $A$ of a circle of radius $5$ cm. meets a line through the centre $O$ at a point $B$, so that $OB$ $=$ $12$ cm. Then find the length of $AB$.

• A. $\sqrt{119}$ cm
• B. $119$ cm
• C. $\sqrt{126}$ cm
• D. $112$ cm

Answer 1

The correct option is A $\sqrt{119}$ cm

In figure, $AB$ is the tangent of circle $(O,r)$.
Here $r$ $=$ $5$ cm. $=$ $AO$ and $OB$ $=$ $12$ cm.
Since tangent is perpendicular to radius $OA$, therefore $OAB$ is a right triangle.
Now in rt $\Delta$ OAB, $\angle A={90}^{\circ }$
Thus $O{B}^2=O{A}^2+A{B}^2$
$\Rightarrow {12}^2=5^2+A{B}^2$
$\Rightarrow A{B}^2=144-25=119$
Therefore, $AB=\sqrt{119}$ cm