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]

\(\mathbf{4b}\) \((301)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-2.298915279258&{}:{}&-5.337757047845&{}:{}&8.636672327103&,\\B^\prime&{}\approx{}&0.297463005165&{}:{}&0.221231742082&{}:{}&0.481305252753&,\\C^\prime&{}\approx{}&0.024005533170&{}:{}&-0.024005533170&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}8.636672327103\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.481305252753\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.038841768588\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.618033988750&{}:{}&-0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.087571481518&{}:{}&-0.058754093781&{}:{}&0.971182612263&. \end{alignedat} \]
4b (301)

Hiroyasu Kamo