Comparing two geometric problems 
Applet, mono version
This applet deals comprehensively with hexlet.
This applet uses Javaview
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In this applet, there is great flexibility to choose radii, transparencies, etc., which allows you to clearly see the effect of the transformation used in the proof - an inversion centered at the tangency point of the blue and red surfaces - to reduce the question to a simpler one, with two planes instead of two spheres:
