If the vertices of a polyhedron are on the same sphere, then the polyhedron is called the inner polyhedron of the ball, and the ball is called the outer receiving ball of the polyhedron The problem of the polyhedron external ball is a key and difficult point in three-dimensional geometry, and it is also a hot spot in the college entrance examination The students' spatial imagination ability and naturalization ability are tested The key to solving this kind of problem is to grasp the characteristics of injunction, that is, the distance from the center of the sphere to the vertex of the polyhedron is equal to the radius of the sphere, and special attention should be paid to the relationship between the relevant geometric elements of the polyhedron and the radius of the sphere, and the method of finding the radius of the polyhedron external ball often plays a vital role in the solution
The inscribed problem of the ball mainly refers to the inscribed polyhedron and the rotating body of the sphere, and the solution should first find the tangent point and solve it by making a cross-section If the inscribed is a polyhedron, then when making a cross-section, it is mainly grasped by the diagonal plane of the polyhedron over the center of the sphere When the ball is tangent to each face of the polyhedron, pay attention to the distance from the center of the sphere to each face, that is, the radius of the ball, when finding the radius of the ball, the center of the sphere can be connected with the vertices of the polyhedron, the radius of the ball is the height of the small pyramid into which it is divided, and the radius of the ball is found by the volume method
[Method Summary].
The wall corner model is a triangular pyramid with a side edge perpendicular to the bottom surface and the bottom surface is a right-angled triangle model, which is solved by the construction method (constructing a box) The diameter of the receiving ball is equal to the diagonal length of the body of the box (the three edges at the same vertex of the cuboid are a, b, and c, respectively, and the radius of the outer ball is r,
There are four types of problems that can be solved by finding the radius of the ball:
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