Question

Length of a tangent segment draw 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 C $7cm$

Let external point be $B$. $OA$ be radius of circle.

Given:

$OB=12.5cm$

$AB=12cm$

In right triangle, $AOB$, by Pythagoras Theorem,

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

$A{O}^2=O{B}^2-O{A}^2={12.5}^2-{12}^2=12.25$

$\therefore AO=3.5cm$

$Diameter=2\left(AO\right)=2\left(3.5\right)=7cm$