Derousseau's Generalization of the Malfatti circles

\(A=36\degree\), \(B=36\degree\), \(C=108\degree\).

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

\(\mathbf{6b}\) \((321)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&5.916949268008&{}:{}&7.955791036595&{}:{}&-12.872740304603&,\\B^\prime&{}\approx{}&-0.021069802915&{}:{}&1.055161460168&{}:{}&-0.034091657253&,\\C^\prime&{}\approx{}&-0.642039521920&{}:{}&0.642039521920&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-12.872740304603\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.034091657253\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.038841768588\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.618033988750&{}:{}&-0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.080000361019&{}:{}&1.129443303240&{}:{}&-0.049442942222&. \end{alignedat} \]
6b (321)

Hiroyasu Kamo