MathDB

Given a triangular pyramid in which all the plane angles at one of the vertices are right. It is known that there is a point in space located at a distance of

3

from the indicated vertex and at distances

\sqrt5, \sqrt6, \sqrt7

from three other vertices. Find the radius of the sphere circumscribed around this pyramid. (The circumscribed sphere for a pyramid is the sphere containing all its vertices.)

Problem Statement