Descartes' circle theorem | Soddy's formula (English)
Search for " Descartes' circle theorem " OR " Soddy's formula " in NRICH | PLUS | maths.org | Google
Definition (undergraduate level)
If we draw four circles A, B, C, D so that they do not overlap but each touches the other three, and if we call the radii of the circles r1, r2, r3, r4, and let b1=1/r1, etc, then ( b1 + b2 + b3 + b4 ) 2 = 2 ( b1 2 + b2 2 + b3 2 + b4 2 ).
Relations
- broader:
- (en) Theorem
- references:
- (en) Circle
- (en) Radius
- see also:
- (en) Apollonius' problem
Funded by: EU Socrates Minerva, HeyMath!, Cambridge University Press