Question

Two circles of radius $3$ and $4$ units are drawn and the distance between their centres is $5$ units. Find the length of their direct common tangent.

• A. $6$
• B. $12$
• C. $7$
• D. $2\sqrt{6}$

Answer 1

The correct option is D $2\sqrt{6}$

Length of direct common tangent $=\sqrt{d^2-(r_1-r_2{)}^2}$
$=\sqrt{5^2-(4-3{)}^2}$
$=\sqrt{25-1}=2\sqrt{6}$ units

So, option D is correct.