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!