Question

Length of a tangent segment drawn from a point which is at a distance $12.5cm$ from the centre of a circle is $12cm$, find the diameter of the circle.

• A. $25cm$
• B. $24cm$
• C. $7cm$
• D. $14cm$

Answer 1

The correct option is A $25cm$

In $△PAO$:

Applying pythagoras theorem

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

$\Rightarrow {12}^2+r^2=(12.5{)}^2$

$\Rightarrow r^2=156.25-144$

$\Rightarrow r^2=12.25$

$\Rightarrow r=\sqrt{12.25}cm$