Explanation:

When two circles touch externally, it means that they touch each other at exactly one point from the outside. In this situation, we can determine the number of common tangents between the two circles.

Definition:
A tangent is a straight line that touches a circle at exactly one point. Common tangents are the tangents that are common to both circles.

Case 1: No common tangents
If the two circles are of different sizes, and the smaller circle is completely enclosed in the larger circle, then there will be no common tangents between the circles. In this case, the answer would be 0.

Case 2: One common tangent
If the two circles are of the same size and touch each other externally, then there will be exactly one common tangent between the circles. The tangent will touch both circles at the point where they touch each other.

Case 3: Two common tangents
If the two circles are of different sizes and touch each other externally, then there will be exactly two common tangents between the circles. These tangents will touch both circles at the point where they touch each other, but they will be on opposite sides of the point.

Case 4: Three common tangents
If the two circles are of the same size and intersect each other, then there will be exactly three common tangents between the circles. These tangents will touch both circles at the points where they intersect each other.

Case 5: Four common tangents
If the two circles are of different sizes and intersect each other, then there will be exactly four common tangents between the circles. These tangents will touch both circles at the points where they intersect each other, and they will be on opposite sides of the points.

In the given question, it is mentioned that the two circles touch externally. Therefore, the number of common tangents between the circles will be 3 (option B).