Morpomatic

Four circles related

There is a general relation between the radiuses of four circles and the angles between then. This comes from an even more general relation between circles, but the relation here has many of the qualities of the type. The relation is given in terms of a determinant

Theorem: Given four circles with inverse radiuses r₁, r₂, r₃ and r₄ and distangles v_p,q. Then the relation of the inverse radiuses and the distangles are given by

This type can take many shapes. The radiuses of the circles can take special values, and so can the distangles between them.

Ongoing consideerations

On this side there is a demonstration of the general formula that comes from the determinant. This formula can be calculated with the determinant calculater. On other sides spesial variation of teh theorem is given.

The orthogonal species

The Descartes when one circle is a line.

Four circles examples

Values:

u:		v:		w:
r:		s:		t:

a²t² - a² + a²w² - 2a²w s t + a²s² + 2 a b u - 2 a b u t² - 2 a c u w + 2 a d u w t + 2 a c u s t - 2 a d u s - 2 a b v w + 2 a b v s t + 2 a c v - 2 a d v t - 2 a c v s² + 2 a d v w s + 2 a b w r t - 2 a b r s - 2 a c r t + 2 a d r + 2 a c w r s - 2 a d w²r - b² + b²t² + 2 b c w - 2 b d w t - 2 b c s t + 2 b d s + b²v² - 2 b²v r t - 2 b c u v + 2 b d u v t + 2 b c v r s - 2 b d v²s + b²r² + 2 b c u r t - 2 b d u r - 2 b c w r² + 2 b d v w r - c² + 2 c d t + c²s² - 2 c d w s + c²u² - 2 c d u²t - 2 c²u r s + 2 c d u v s + 2 c d u w r + c²r² - 2 c d v r - d² + d²w² + d²u² - 2 d²u v w + d²v²

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Morphomatic

Four circles related

Ongoing consideerations

Four circles examples

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