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]

\(\mathbf{7b}\) \((323)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.505310785923&{}:{}&4.053678004005&{}:{}&-6.558988789928&,\\B^\prime&{}\approx{}&-0.010735600801&{}:{}&1.028106167787&{}:{}&-0.017370566986&,\\C^\prime&{}\approx{}&-0.665147500340&{}:{}&0.665147500340&{}:{}&1.000000000000&. \end{alignedat} \]
7b (323)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-6.558988789928\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.017370566986\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.076231263082\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.618033988750&{}:{}&-0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
7b (323)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.040692322547&{}:{}&1.088335723635&{}:{}&-0.047643401087&. \end{alignedat} \]
7b (323)

Hiroyasu Kamo