1) Grasp the key features of "connection" and "cutting"

A) receiving the ball from the outside

The key feature of external capture is external "capture". Therefore, the distance from each "connecting line" point to the center of the ball is equal, which is equal to the radius. When solving problems, both drawing and calculation should be used well.

B) inscribed ball

The key feature of inscribed ball is internal "cutting". Therefore, the distance between each "tangent" point and the center of the ball is equal to or equal to the radius, and the connecting line with the center of the ball is perpendicular to the tangent plane, so we should make good use of this point when solving problems, whether drawing or calculating.

2) Grasp the characteristics of "central position"

In this kind of problems, because of some properties of the assembly (such as symmetry), the center of the assembly is often located in some special positions (such as the center coincides with the center), so it is very important to determine the center position in many cases. The general method is:

A) Determining the center position is generally the key first step to solve the problem.

When it is an outer ball or only an inner ball, the center of assembly is the center of the ball; When there are more than one inscribed ball and they are tangent to each other, the center position can be determined according to the symmetry and the center perpendicular of the inscribed surface of the inscribed ball.

B) Establishing geometric figures is generally the key to solving problems (then you only need to calculate the basic quantity and substitute it into the formula to solve it).

Based on the position and center of the sphere (when it is not coincident with the center of the sphere), combined with the tangent point or the inner point, a geometric figure which can be easily used to assist calculation is constructed-the final target is mostly a right triangle. This is the key and skill to solve this kind of problem.