Three tangent circles calculator

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Area between three tangent circles

We define: | a = r2 + r3 | b = r1 + r3 | c = r1 + r2 |
The area of triangle ABC is: | |
The sectors area are: |
And the area between the 3 tangent circles (green area) is:
A = AT − AA − AB − AC
The angles of the triangle ABC can be found by cosine law:
The green area circumference is: | P = α r1 + β r2 + γ r3 |
The radii of the four tangent circles are related to each other according to Descartes circle theorem:
The plus sign means externally tangent circle like circles r1 , r2 , r3 and r4 and the minus sign is for internally tangent circle like circle r5 in the drawing in the top.
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And the curvature of the circles k4 and k5 which are called the Soddy circles are:
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If circle r1 is a straight line then r1 = ∞ and the curvature is k1 = 1 / r1 = 0 The curvature of the two red Soddy circles are simply: |
Area between three tangent circles example

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First, we will find the value of d
![]() ![]() The area of the trapezoid BCDE is:
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The circumference of the green area is: | ![]() |

NOTE: in all the calculations we assumed that r2 > r3