If the two circles are tangent to each other,
then it must be at the same point.
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If the circles have the same radius then an infinite number, and if they do not, then none.
A line joining the centres of two tangent circles also passes through the point of tangency.
They are the common tangents to the circles.
Concentric circles are the circles with the same center therefore they do not cross with each other as the "center is not considered a point on the circle". An exception would be two circles that are concentric and have the same radius, in which case the circles are indistinct and every point of the circles is an intersection.
it intersects the segment joining the centers of two circles