Question

Two circles of radii $8cm$ and $3cm$ have a direct common tangent of length $10cm$. The distance between their centres, upto two places of decimal, is

• A. $11.18cm$
• B. $12.18cm$
• C. $11.38cm$
• D. $12.38cm$

Answer 1

The correct option is A $11.18cm$

Radius of first circle $AB=8cm$

Radius of first circle $DC=3cm$

Length of common direct tangent $BC=10cm$

We need to find the distance between their centers means $AD$.

$\Rightarrow$ Length of direct tangent $=\sqrt{(AD{)}^2-(AB-DC{)}^2}$

$\Rightarrow$ $10=\sqrt{(AD{)}^2-(8-3{)}^2}$

$\Rightarrow$ $10=\sqrt{(AD{)}^2-(5{)}^2}$

$\Rightarrow$ $100=(AD{)}^2-25$

$\Rightarrow$ $100+25=(AD{)}^2$

$\Rightarrow$ $(AD{)}^2=125$

$\Rightarrow$ $AD=5\sqrt{5}cm$

$\therefore$ $AD=11.18cm$

Hence, the distance between two centers of a circle is $11.18cm$.