If the radius  of two circles are 4.5 cm and 3.5 cm and the length of the transverse common tangent is 6 cm, then the distance between the two centers will be:

Correct option is B

Given:

Radius of the two circles: ( r$$_1$$​ = 4.5 ) cm and ( r$$_2$$​ = 3.5) cm

Length of the transverse common tangent = 6 cm

Formula Used:

Formula for the length of the transverse common tangent:

​$$\text{Length} = \sqrt{d^2 - (r_1 + r_2)^2}$$​​

Solution:

$$6 = \sqrt{d^2 - (4.5 + 3.5)^2} \\ \ \\ 6 = \sqrt{d^2 - 8^2} \\ \ \\ 6 = \sqrt{d^2 - 64}\\ \ \\6^2 = d^2 - 64 \\ \ \\ 36 = d^2 - 64 \\ \ \\ d^2 = 100 \\ \ \\ d = 10 \text{ cm}$$​