Question

The centres of two circles with radii 8 cm and 3 cm are 13 cm apart. A direct common tangent touches the circle at A and B respectively then the length of AB is

• A. 8 cm
• B. 10 cm
• C. 12 cm
• D. 14 cm

Answer 1

The correct option is C 12 cm

Given radius of two circle is 8 cm and 3 cm and distance between the centers are 13 cm

Then length of direct common tangent=$\sqrt{d^2-(r_1^2-r_2^2)}=\sqrt{(13{)}^2-\left(\right(8{)}^2-\left(3{)}^2\right)}=\sqrt{169-25}=\sqrt{144}$

Then d=12

Then AB =12 cm