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]

\(\mathbf{2a}\) \((031)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.221231742082&{}:{}&0.297463005165&{}:{}&0.481305252753&,\\B^\prime&{}\approx{}&-5.337757047845&{}:{}&-2.298915279258&{}:{}&8.636672327103&,\\C^\prime&{}\approx{}&-0.024005533170&{}:{}&0.024005533170&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.481305252753\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}8.636672327103\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.038841768588\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.618033988750&{}:{}&0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.058754093781&{}:{}&0.087571481518&{}:{}&0.971182612263&. \end{alignedat} \]
2a (031)

Hiroyasu Kamo