Two circles have radii of 12 cm and 4 cm. If the length of a direct common tangent is 15 cm, what is the distance between their centers?

Correct option is B

​Given :

Radii of circles: R = 12 cm and r = 4 cm

Length of direct common tangent: L = 15 cm

Formula Used :

For a direct common tangent between two circles:
​$$L^2 = d^2 - (R - r)^2$$​​
where d = distance between centers.

Solution: 

$$15^2 = d^2 - (12 - 4)^2 \\ \ \\225 = d^2 - 8^2 \\ \ \\225 = d^2 - 64\\ \ \\d^2 = 225 + 64 = 289 \\ \ \\d = \sqrt{289} = 17 \text{ cm}$$​​