Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{0b}\) \((101)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.868347502413&{}:{}&-0.179840656176&{}:{}&0.311493153763&,\\B^\prime&{}\approx{}&0.744962785747&{}:{}&-1.035276180410&{}:{}&1.290313394663&,\\C^\prime&{}\approx{}&0.349396052863&{}:{}&-0.349396052863&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.311493153763\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}1.290313394663\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.605171715523\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.577350269190&{}:{}&-0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.654398348313&{}:{}&-0.419023491590&{}:{}&0.764625143278&. \end{alignedat} \]
0b (101)

Hiroyasu Kamo