True or False

If two circles have 4 common tangents, then the two circles intersect.

False

Draw a pair of intersecting circles and attempt to draw tangents, then
Draw a pair of non-intersecting circles. Were you able to draw 4 tangents? I was.

Take it one step further , ....
What if one circle is completely contained within a larger circle ?

Ok that's what I thought...thanks!

False.

To determine whether two circles intersect, we need to check if the distance between their centers is less than the sum of their radii. If the two circles have 4 common tangents, it means that the circles are externally tangent to each other at 4 points. However, it doesn't guarantee that the two circles intersect.

Imagine two circles with equal radius, positioned close to each other such that they are tangent at four points. In this case, the distance between their centers will be equal to the sum of their radii, resulting in them not intersecting.

Therefore, having 4 common tangents does not necessarily imply that two circles intersect.