The maximum number of common tangents that can be drawn to two given circles is

The maximum number of common tangents that can be drawn to two given circles is 4.

Here's the step by step explanation:

1. If the two circles are separate (not touching each other), then you can draw 4 common tangents. Two of these are direct tangents, where each touches both circles at a single point, and the other two are transverse tangents, where each touches the two circles at two distinct points.

2. If the two circles touch each other externally (i.e., they have one point in common), then you can draw 3 common tangents. Two of these are direct tangents and one is a common internal tangent.

3. If the two circles intersect (i.e., they have two points in common), then you can draw 2 common tangents. Both of these are direct tangents.

4. If one circle lies completely inside the other, then you can draw only 1 common tangent if they touch each other internally (i.e., they have one point in common). If they don't touch each other, then you can't draw any common tangents.

So, the maximum number of common tangents that can be drawn to two given circles is 4.