Tangency means that the tangent slope (first derivative) of two curves at the intersection point is the same, and the two curves do not overlap near this point. If a straight line intersects a curve at two points, and the two points are infinitely close and tend to overlap, then the straight line is the tangent of the curve at that point. In junior high school mathematics, if a straight line is perpendicular to the radius of a circle and passes through the outer end of the radius of the circle.
A straight line connecting two centers of the circle is called a connecting line. When two circles are tangent, the tangent point is on the connecting line.
When two circles circumscribe each other, is the center distance o? o？ =R﹢r。 (Let the radius of the big circle be R and the radius of the small circle be R)
When two circles are inscribed, the center distance o? o？ =R﹣r .
The straight line connecting two circles or its extension line must pass through the tangent point.
Geometric definition
P and Q are two adjacent points on curve C, and P is a fixed point. When point Q is infinitely close to point P along curve C, the limit position PT of secant PQ is called the tangent of curve C at point P, and point P is called the tangent point. A straight line PN passing through the tangent point P and perpendicular to the tangent line PT is called the normal of the curve C at the point P (the idea of infinite approximation).
Note: In plane geometry, a straight line with only one common intersection with a circle is called the tangent of the circle. This definition does not apply to general curves. PT is the tangent of curve C at point P, but it has another intersection with curve C; On the contrary, although the straight line L has only one intersection with the curve C, it is not the tangent of the curve C. ..