Diameter of inscribed circle

Question

incribed circle

How can i express diameter of inscribed circle in terms of radius of three circles.

@achillehui: Very interesting! – georg Jul 18 '14 at 13:06 — georg, Jul 18 '14 at 13:06

georg · Accepted Answer · 2014-07-18T09:10:34.970

2

$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.

edited Jul 18 '14 at 09:10

answered Jul 18 '14 at 09:05

georg

1 Answers1