Two circles are of radii 7 cm and 2 cm their centres being 13 cm apart. Then the length of direct common tangent to the circles between the points of contact is

Answer: Option A

According to question
Given:

OO' = 13 cm
OA = 7 cm
O'B = 2 cm
∴ Length of direct common tangent
$$\begin{array}{rl}& \text{AB}=\sqrt{{\left({\text{OO}}^{\prime }\right)}^2-{\left(\text{R}-\text{r}\right)}^2}\\ & \text{AB}=\sqrt{{\left(13\right)}^2-{\left(7-2\right)}^2}\\ & \text{AB}=\sqrt{169-25}\\ & \text{AB}=\sqrt{144}\\ & \text{AB}=12\text{ cm}\end{array}$$