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A triangle that fits on a sphere

Source: Spanish Mathematical Olympiad 1965 P6

November 15, 2016

geometry3D geometrysphere

Problem Statement

We have an empty equilateral triangle with length of a side

l

. We put the triangle, horizontally, over a sphere of radius

r

. Clearly, if the triangle is small enough, the triangle is held by the sphere. Which is the distance between any vertex of the triangle and the centre of the sphere (as a function of

l

and

r

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