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]

\(\mathbf{4c}\) \((310)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&58.462170210314&{}:{}&67.781251278963&{}:{}&-125.243421489277&,\\B^\prime&{}\approx{}&0.442845925067&{}:{}&1.375426647384&{}:{}&-0.818272572451&,\\C^\prime&{}\approx{}&0.783227248675&{}:{}&0.783227248675&{}:{}&-0.566454497351&. \end{alignedat} \]
4c (310)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}10.319081068649\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.067419277683\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.119239248638\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \]
4c (310)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.126528029260&{}:{}&1.672613439834&{}:{}&-1.799141469094&. \end{alignedat} \]
4c (310)

Hiroyasu Kamo