Derousseau's Generalization of the Malfatti circles

\(A=30\degree\), \(B=30\degree\), \(C=120\degree\).


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

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-1.035276180410&{}:{}&0.744962785747&{}:{}&1.290313394663&,\\B^\prime&{}\approx{}&-0.179840656176&{}:{}&0.868347502413&{}:{}&0.311493153763&,\\C^\prime&{}\approx{}&-0.349396052863&{}:{}&0.349396052863&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.290313394663\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.311493153763\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.605171715523\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.577350269190&{}:{}&0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.419023491590&{}:{}&0.654398348313&{}:{}&0.764625143278&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo