How can i express diameter of inscribed circle in terms of radius of three circles.
2026-04-24 14:22:24.1777040544
Diameter of inscribed circle
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1
$a=\frac{1}{R_1},\, b=\frac{1}{R_2},\, c=\frac{1}{R_3},\, x=\frac{1}{R},\, $ then
$x = a+b+c+2\sqrt{ab+bc+ac}$
I don't know derivation of this relationship. Discovered him famous British chemist F. Soddy.
This relationship is known from Czech books on recreational mathematics from 1967.