Tangent circles are circles that touch one another without crossing. The distance between the centres of the circles must be equal to the difference or the sum of their radii.
"Tangent" to a circle means touching the circle at one point, and only one point.
Think of a skinny bicycle wheel standing on the ground. The ground is 'tangent' to the wheel.
A circle's tangent is exactly the same as a triangle's tangent. If you look at a circle, you can make the radius the hypotenuse. Then make a vertical line from the point, and a horizontal line from...