四面体外接球半径的求法,一直以来不尽相同,如对称法、长方体模型法等,但其方法没有规律性,很难直接判断。一旦常规方法无法入手,只能利用空间直角坐标系中的距离公式进行求解,计算量极大。在此,笔者从几种特殊情况入手,给出一种较为简易的求解四面体外接球半径的通法。例1已知四面体P-ABC,PA⊥底面ABC,AB⊥AC,设PA=h,AC=b,AB=c,求该四面体的外接球半径。 Tetrad external ball radius of the law has been different, such as symmetry, cuboid model method, but its method is not regular, it is difficult to judge directly. Once the conventional method can not start, can only use the space Cartesian coordinate system to solve the distance formula, a huge amount of computation. Here, I start from several special cases, gives a more simple method to solve tetrahedron external ball radius of the law. Example 1 Known tetrahedron P-ABC, PA⊥ bottom ABC, AB ⊥ AC, with PA = h, AC = b, AB = c, seek the outer sphere of the tetrahedron radius.