Question

TOUGH GEOMETRY QUESTION http://puu.sh/1lMYq

Answer 1

Whew, that's a beauty!

Answer 2

Hmm... it really is. :P

I guess just to toss some ideas out there, but for the sphere to be placed inside that space, it would be tangent to: A) all three cones, and B) the plane containing the vertices of the three cones. Perhaps that could be useful somehow...

Answer 3

I think that (B) ^ you mention helps a lot.

Answer 4

* And the distance to all four of those locations from the center are the same

Answer 5

I have a feeling similar triangle proportions could also be useful.

Answer 6

how about passing a plane containing the height of one cone and the center of the cylinder. on that plane is an isosceles triangle and a circle.

Answer 7

Hmm.. something like this? Although it is a sphere. I can see some angles we can find with trig here pretty easily also

Answer 8

the projection of the center of the circle tn the plane containing the three centers of the bases is the centroid of the equilateral trianlge formed by the centers of the bases.

Answer 9

Hmm.. actually, I believe we could also determine the length of the segment from the vertex of this triangle to the sphere using that fact ^, and then use trigonometry with the angle to find the radius...