Two non-intersecting (externally disjoint) circles: how many common tangents can be drawn?

Introduction / Context:
Given two circles, the number of common tangents depends on whether they intersect, are disjoint externally, or one lies completely inside the other. Recognising these cases is standard geometry knowledge.

Given Data / Assumptions:

• “Non-intersecting circles” interpreted as disjoint externally (neither touching nor one inside the other).

Concept / Approach:
For two externally disjoint circles, there are two direct (external) tangents and two transverse (internal) tangents, totalling four. If one circle is inside the other without touching, there are 0 transverse and 2 direct tangents (not our case).

Step-by-Step Solution:
Classify: disjoint externally ⇒ 2 direct + 2 transverse = 4.

Verification / Alternative check:
Sketching two separate circles quickly reveals the two pairs of tangents.

Why Other Options Are Wrong:
3 is impossible by symmetry; 2 corresponds to concentric/contained case; 13 is nonsensical.

Common Pitfalls:
Misreading “non-intersecting” to include “one inside another”; here we use the standard “externally disjoint” meaning.

Final Answer:
4