Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{6a}\) \((231)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.055161460168&{}:{}&-0.021069802915&{}:{}&-0.034091657253&,\\B^\prime&{}\approx{}&7.955791036595&{}:{}&5.916949268008&{}:{}&-12.872740304603&,\\C^\prime&{}\approx{}&0.642039521920&{}:{}&-0.642039521920&{}:{}&1.000000000000&. \end{alignedat} \]
6a (231)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.034091657253\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-12.872740304603\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.038841768588\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.618033988750&{}:{}&0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
6a (231)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.129443303240&{}:{}&-0.080000361019&{}:{}&-0.049442942222&. \end{alignedat} \]
6a (231)

Hiroyasu Kamo