Two identical balls of radius $\sqrt{15}$ and two identical balls of a smaller radius are located on a plane so that each ball touches the other three. Find the area of the surface $S$ of the ball with the smaller radius.
Problem
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Tags: geometry, 3D geometry, sphere, tangent
Boris_G
31.03.2021 08:14
this is similar to an aime problem i have seen before
vanstraelen
01.04.2021 21:27
The ball with the smaller radius $r=(2-\sqrt{3})\sqrt{15}$.
Honestly
02.04.2021 03:47
bumppppppp
Honestly
06.04.2021 03:51
bumppppp I don't think the tetrahedron that has vertices on the centers of the spheres reveals any important information, so I am stumped.
natmath
06.04.2021 04:15
Doesn't n dimensional descartes kill the problem?
Bobcats
06.04.2021 04:16
It's literally just Pythagorean Theorem. $r^2 + (\sqrt{15})^2 + (\sqrt{15}-r)^2 = (r+\sqrt{15})^2$.