Question

A tangent of length $12\text{cm}$ is drawn to the circle of radius $5$ cm from point $A$. Find out the distance between the point $A$ and the centre of the circle.

• A. $13$ cm
• B. $14$ cm
• C. $17$ cm
• D. $15$ cm

Answer 1

The correct option is A $13$ cm

Concept: Tangents to a circle are perpendicular to the radius of the circle.


So, $△ABO$ is right triangle right angled at $B$.
$OB=5$ cm (radius of circle)
$AB=12$ cm (length of tangent)
$OA=\text{Distance between point A and center of the circle}$

Now, applying pythagoras theorem,
$O{A}^2=O{B}^2+A{B}^2$
$O{A}^2=5^2+{12}^2$
$O{A}^2=25+144$
$O{A}^2=169$
$OA=\sqrt{169}$
$OA=13$ cm

Distance between the point $A$ and the center is $13$ cm.
So, option $\left(a\right)$ correct.