Question

Three non-overlapping, non-touching circles are drawn in a plane. What is the maximum number of distinct common tangents that can be drawn to them in total?

• A. 17
• B. 16
• C. 9
• D. 12

Answer 1

Answer:

D. 12

There are 3 pairs of circles:

• Circle 1 & Circle 2 → 4 tangents

• Circle 1 & Circle 3 → 4 tangents

• Circle 2 & Circle 3 → 4 tangents

Therefore,

$3\times4=\boxed{12}$

✅ Answer: 12