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.
Sure. They would have one of two appearances. Either they look like a figure ' 8 ' with a line across the middle, or else they look like two soap bubbles, one inside the other, hanging from the line.
Yes.
Two circles in the same plane are externally tangent if they intersect in exactly one point and their intersection of their interiors is empty.
Tangent circles.
... touches each circle in exactly one point on each circle. given any two circles where none is entirely inside or inside and tangent to the other, there are at most four straight lines that are tangent to both circles.
You join the centres of the two circles. Divide this line in the ratio of the two radii. Draw the tangent from this point to either circle and extend it to touch the other circle.
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.
If the tangent circles are outside of one another, then neither passes through the center of the other. If one circle is within the other, then the inner tangent circle might contain the center point of the larger circle. There will be infinitely many inner tangent circles that do not.
Concentric circles
They are the common tangents to the circles.
When the centers of both the circles are at the same point.
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.