Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{4c}\) \((310)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&22.329336426955&{}:{}&29.136415405085&{}:{}&-50.465751832040&,\\B^\prime&{}\approx{}&0.297341324655&{}:{}&1.217668956838&{}:{}&-0.515010281493&,\\C^\prime&{}\approx{}&0.633974596216&{}:{}&0.633974596216&{}:{}&-0.267949192431&. \end{alignedat} \]
4c (310)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}7.807078978130\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.079672367818\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.169872981078\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&3.732050807569&{}:{}&3.732050807569&{}:{}&-6.464101615138&. \end{alignedat} \]
4c (310)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.803317803221&{}:{}&1.364352042889&{}:{}&-1.167669846111&. \end{alignedat} \]
4c (310)

Hiroyasu Kamo