Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{1b}\) \((103)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.923990395078&{}:{}&-0.103831051254&{}:{}&0.179840656176&,\\B^\prime&{}\approx{}&0.430104464888&{}:{}&-0.175067250635&{}:{}&0.744962785747&,\\C^\prime&{}\approx{}&1.027821446333&{}:{}&-1.027821446333&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.179840656176\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.744962785747\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}1.780238966158\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.577350269190&{}:{}&-0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.762803932467&{}:{}&-0.287587527212&{}:{}&0.524783594745&. \end{alignedat} \]
1b (103)

Hiroyasu Kamo