Question

The length of the transverse common tangent to two circles of radii $8$ cm and $3$ cm, the centres of the circles be at a distance $13$ cm is

• A. $\sqrt{3}cm$
• B. $2\sqrt{3}cm$
• C. $3\sqrt{3}cm$
• D. $4\sqrt{3}cm$

Answer 1

The correct option is D $4\sqrt{3}cm$

Given radii of circles are $8$ cm and $3$ cm and length between circles is $13$ cm. The length of a transverse common tangent =$\sqrt{d^2-(r_1+r_2{)}^2}$

In the quation $r_1=8cm$ and $r_2=3cm$ and $d=13cm$

$=\sqrt{(13{)}^2-(8+3{)}^2}=\sqrt{169-121}=\sqrt{48}$

$\Rightarrow$ the length of common tangent is $=4\sqrt{3}cm$