Derousseau's Generalization of the Malfatti circles

\(A=22.5\degree\), \(B=22.5\degree\), \(C=135\degree\).

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

\(\mathbf{2c}\) \((130)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.375426647384&{}:{}&0.442845925067&{}:{}&-0.818272572451&,\\B^\prime&{}\approx{}&67.781251278963&{}:{}&58.462170210314&{}:{}&-125.243421489277&,\\C^\prime&{}\approx{}&0.783227248675&{}:{}&0.783227248675&{}:{}&-0.566454497351&. \end{alignedat} \]
2c (130)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.067419277683\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}10.319081068649\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.119239248638\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \]
2c (130)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.672613439834&{}:{}&1.126528029260&{}:{}&-1.799141469094&. \end{alignedat} \]
2c (130)

Hiroyasu Kamo