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在平面几何中,不在同一直线上的三点可以确定一个圆:若三点连线组成三角形,且三角形的三边己知,则此三角形的外接圆的半径可以求出。在空间中不在同一平面内的四点可以确定一个球,若四点连线组成四面体,且四面体的六条棱长已知,那末此四面体的外接球半径是否可以求出?本文对此问题进行探索。设四面体D—ABC中,BC=a、AC=b、AB=c其相对棱DA、DB、DC的长分别为a、b、c,求DABC的外接球的半径。解:在平面ABC中过A作AE⊥BC于E,在平面DBC中过D作DF⊥BC于F,则平面ABC与平面DBC所成二面角的平面角,是异面直线DF与AE所成的角,或此角的补角,由于棱长已知,所以各个
In plane geometry, three points that are not on the same line can determine a circle: If three lines form a triangle and the three sides of the triangle are known, the radius of the circumcircle of the triangle can be found. A ball can be determined at four points in space that are not in the same plane. If the four-point line forms a tetrahedron and the length of the six edges of the tetrahedron is known, then can the radius of the circumcircle of this tetrahedron be determined? Questions to explore. Let tetrahedron D-ABC, BC = a, AC = b, AB = c relative to the length of the DA, DB, DC, respectively, a, b, c, DABC circumscribed ball radius. Solution: In plane ABC, A is AE⊥BC in E. In plane DBC, D is DF⊥BC in F. The plane angle formed by plane ABC and plane DBC is the dihedral line DF and AE. The angle formed, or the complement angle of this angle, is due to the known length of the ridge, so each