Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{6c}\) \((330)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.577350269190&{}:{}&0.788675134595&{}:{}&-1.366025403784&,\\B^\prime&{}\approx{}&0.788675134595&{}:{}&1.577350269190&{}:{}&-1.366025403784&,\\C^\prime&{}\approx{}&0.405945781451&{}:{}&0.405945781451&{}:{}&0.188108437098&. \end{alignedat} \]
6c (330)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.211324865405\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.211324865405\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.108772844311\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&3.732050807569&{}:{}&3.732050807569&{}:{}&-6.464101615138&. \end{alignedat} \]
6c (330)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.874005200027&{}:{}&0.874005200027&{}:{}&-0.748010400053&. \end{alignedat} \]
6c (330)

Hiroyasu Kamo