Explanation:

Alright, let's break this down step by step:

- You’ve got two circles with radii 8 cm and 3 cm. The distance between their centers is 13 cm.

- AB is a direct common tangent—meaning it just grazes both circles at single points A and B, with A on the bigger circle and B on the smaller.

- Here’s the geometry trick: For direct common tangents, the length is

v[D² – (R – r)²],

where D is the distance between centers, R and r are the radii.

- Plugging in:

= v[13² – (8 – 3)²]

= v[169 – 25]

= v144

= 12 cm

- Let’s check options:

1. 10 cm

2. 12 cm

3. 8 cm

4. 6 cm

- Only option 2 fits. The rest don’t check out with the calculation above.