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Math Help - Tangent spheres with triangle

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
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    Tangent spheres with triangle

    I'm having trouble understanding this question, it may be out of my current knowledge base, but I won't know until I try.
    I desire most a diagram to help me visualize the question. If you have a complete solution then leave it as a spoiler.

    Question
    Three spheres are tangent to a plane at the vertices of a triangle and tangent to each other. Find the radii of these spheres if the sides of the triangle are 6, 8, 10.

    Thanks in advance to the forum
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    Hi

    Here is a view of 2 of the 3 spheres and the plan



    One relation between the radii of the 2 spheres is
    (x-y)+a=(x+y) or 4xy=a

    Does this help ?
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