The difference between the radii of the circumscribed and inscribed circles of a regular triangle is equal to m, express the side of this triangle through m
The radius of a circle inscribed in a regular triangle is expressed by the formula:
r = a / 2√3, where a is the side of the triangle.
The radius of a circle circumscribed about a regular triangle:
R = a / √3.
The difference between these radii m is equal to:
m = R – r = a / √3 – a / 2√3 = a / 2√3.
From here we express the side of this triangle in terms of m: a = 2m√3.
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