The length of the direct common tangent of two circles of radii 2 cm and 8 cm is 8 cm. Then the distance between the centers of the circles is

For two circles with radii r = 2 cm and R = 8 cm, the direct common tangent length L = 8 cm. Using the formula L = √(d² - (R - r)²) where d is the distance between centers: 8 = √(d² - (8 - 2)²) = √(d² - 36). Squaring: 64 = d² - 36, so d² = 100, and d = 10 cm. Option B is correct. Options A (8 cm), C (6 cm), and D (12 cm) are incorrect distances.