Derousseau's Generalization of the Malfatti circles

Equilateral Triangle

\(a:b:c=1:1:1\), \(A=60\degree\), \(B=60\degree\), \(C=60\degree\).


[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-2.398717474236&{}:{}&1.699358737118&{}:{}&1.699358737118&,\\B^\prime&{}\approx{}&-0.366025403784&{}:{}&1.000000000000&{}:{}&0.366025403784&,\\C^\prime&{}\approx{}&-0.366025403784&{}:{}&0.366025403784&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.699358737118\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.366025403784\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.366025403784\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-1.000000000000&{}:{}&1.000000000000&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.672027713219&{}:{}&0.836013856610&{}:{}&0.836013856610&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo