Question

The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its center.

Answer 1

Given:- A circle with center $O$ and $AB$ is the tangent from point $A$.

Radius of circle $=OB=8cm$

Distance of point from the circle $=AO=10cm$

To find:- Length of tangent, i.e., $AB=?$

Solution:-

Since $AB$ is tangent,

Therefore,

$AB\perp OB[\because \text{Tangent at any point of circle is perpendicular to the radius through point of contact}]$

$\Rightarrow \angle ABO=90°$

Hence $△OAB$ is a right angle triangle.

Using pythagoras theorem in $△OAB$,

${AO}^2={AB}^2+{OB}^2$

${\left(10\right)}^2={AB}^2+{\left(8\right)}^2$

$\Rightarrow AB=\sqrt{100-64}=6cm$

Hence the length of tangent is $6cm$.

Hence the correct answer is $6cm$.