Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{3c}\) \((132)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.359681312352&{}:{}&-0.874691593845&{}:{}&1.515010281493&,\\B^\prime&{}\approx{}&-29.713765674275&{}:{}&-20.751986157765&{}:{}&51.465751832040&,\\C^\prime&{}\approx{}&-0.366025403784&{}:{}&-0.366025403784&{}:{}&1.732050807569&. \end{alignedat} \]
3c (132)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.234372906197\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-7.961779516510\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.098076211353\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&3.732050807569&{}:{}&3.732050807569&{}:{}&-6.464101615138&. \end{alignedat} \]
3c (132)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.601583108703&{}:{}&-1.021726569529&{}:{}&2.623309678232&. \end{alignedat} \]
3c (132)

Hiroyasu Kamo