Four 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?

Question

Accepted Answer

1. For two disjoint circles there can be up to $4$ common tangents (two direct and two transverse).

2. Number of pairs among four circles is $\binom{4}{2}=6$.

3. Place the circles so no tangent touches more than two circles. Then tangents add: $6	imes4=24$.

4. So the maximum number of distinct common tangents is **24**.

FINAL_ANSWER: d

Answer

Answer

Answer