39each is tangent to other two
Let s1, s2, s3 be 3 tangent spheres each with each. These spheres are placed on a table, and their radii are 1,2,3 respectively. A plane tangent to all these spheres is considered. What is the angle made by this plane with the plane of the table (on which the 3 spheres lie)?
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4 Answers
39Here goes:
Because of the symmetry the plane containing the centers of the spheres is the bisector plane of the angle you want to calculate. The triangle formed by the centers of the spheres (call them A,B,C) is projected on the table as
the triangle formed by the points of tangency to the table (call them A1,B1,C1). It's not hard to calculate the sides of the 2 triangles, so you can easily get their areas. But you know that S(A1B1C1)=S(ABC)*cos(the angle between the planes ABC & A1B1C1), so you can find this angle, which is half the angle we want.