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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 & Solution
Correct Answer:
Option
A
According to question
Given:
OO' = 13 cm
OA = 7 cm
O'B = 2 cm
∴ Length of direct common tangent
$$\eqalign{ & {\text{AB}} = \sqrt {{{\left( {{\text{OO}}'} \right)}^2} - {{\left( {{\text{R}} - {\text{r}}} \right)}^2}} \cr & {\text{AB}} = \sqrt {{{\left( {13} \right)}^2} - {{\left( {7 - 2} \right)}^2}} \cr & {\text{AB}} = \sqrt {169 - 25} \cr & {\text{AB}} = \sqrt {144} \cr & {\text{AB}} = 12{\text{ cm}} \cr} $$
Given:
OO' = 13 cm
OA = 7 cm
O'B = 2 cm
∴ Length of direct common tangent
$$\eqalign{ & {\text{AB}} = \sqrt {{{\left( {{\text{OO}}'} \right)}^2} - {{\left( {{\text{R}} - {\text{r}}} \right)}^2}} \cr & {\text{AB}} = \sqrt {{{\left( {13} \right)}^2} - {{\left( {7 - 2} \right)}^2}} \cr & {\text{AB}} = \sqrt {169 - 25} \cr & {\text{AB}} = \sqrt {144} \cr & {\text{AB}} = 12{\text{ cm}} \cr} $$
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