Question

The length of the tangent from an external point, at a distance of 13 cm from the center of the circle of radius 5 cm is

• A. $10cm$
• B. $12cm$
• C. $13cm$
• D. $14cm$

Answer 1

The correct option is B $12cm$

In the given figure $△POA,\angle A={90}^{\circ }$

$\therefore P{O}^2=P{A}^2+A{O}^2$

$\Rightarrow P{A}^2=P{O}^2-A{O}^2$

$\Rightarrow P{A}^2=(13{)}^2-(5{)}^2$

$\Rightarrow PA=\sqrt{196-25}$

$\Rightarrow PA=\sqrt{144}=12cm.$

Hence the length of the tangent is 12 cm.