I'm trying to find the largest sphere that lies inside the tetrahedron whose vertices are the origin and the points A(1, 0, 0), B(0, 1, 0) and C(0, 0,−2).
Any ideas? Thanks!
If it had been a regular tetrahedron with equilateral triangles, the
distance between each side would represent the diameter of the
sphere. In this case, the tetreahdron is not even isoceles and I
have no idea where to start, since I am having a hard time even
visualizng the sphere in the shape.
I first drew the tetrahedron and tried to see if I could visulalize
where the centre of the sphere could be and tried to see if I could
see some formula to find its radius. Also, I calculated the
distances between the points to discover it was not a regular
tetrahedron but instead had distances of 1, sqrt(2), sqrt(5) and 2.
I am thinking it may have to do with the sphere being
tangent to the sides after doing some research, but really have no
idea where to begin testing this. Thanks!