Question

The distance between two centres of two circles having radii $9cm$ and $4cm$ is $13cm$. What is the length of the direction common tangent of these circles?

• A. $12cm$
• B. $11cm$
• C. $10cm$
• D. $9.5cm$

Answer 1

The correct option is A $12cm$

Given that,

Radius of circle Ist $=R_1=9$cm

Radius of circle IInd $=R_2=4$cm

Distance between two centres of two circles$=13$cm

Find:- Common tangent$=?$

Then, We know that,

$D^2=7^2-(R_1-R_2{)}^2$

where $T=$tangent

$D=$distance

$R_1$ and $R_2$ be the radii of two circles.

So, $D^2=T^2-(R_1-R_2{)}^2$

$(13{)}^2=T^2-(9-4{)}^2$

$169=T^2-5^2$

$169-25=T^2$

$T^2=144$

$T^2={12}^2$

$T=12$cm

Hence, the common tangent$=12$cm.