Derousseau's Generalization of the Malfatti circles

\(A=36\degree\), \(B=36\degree\), \(C=108\degree\).

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

\(\mathbf{3b}\) \((123)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&2.680881290508&{}:{}&2.719723059095&{}:{}&-4.400604349603&,\\B^\prime&{}\approx{}&-0.151564971415&{}:{}&1.396802246667&{}:{}&-0.245237275253&,\\C^\prime&{}\approx{}&-1.878107499420&{}:{}&1.878107499420&{}:{}&1.000000000000&. \end{alignedat} \]
3b (123)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-4.400604349603\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.245237275253\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-3.038841768588\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.618033988750&{}:{}&-0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
3b (123)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.068234650416&{}:{}&1.824968519586&{}:{}&-0.756733869169&. \end{alignedat} \]
3b (123)

Hiroyasu Kamo