Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{1a}\) \((013)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.175067250635&{}:{}&0.430104464888&{}:{}&0.744962785747&,\\B^\prime&{}\approx{}&-0.103831051254&{}:{}&0.923990395078&{}:{}&0.179840656176&,\\C^\prime&{}\approx{}&-1.027821446333&{}:{}&1.027821446333&{}:{}&1.000000000000&. \end{alignedat} \]
1a (013)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.744962785747\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.179840656176\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}1.780238966158\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.577350269190&{}:{}&0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
1a (013)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.287587527212&{}:{}&0.762803932467&{}:{}&0.524783594745&. \end{alignedat} \]
1a (013)

Hiroyasu Kamo