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]

\(\mathbf{7a}\) \((233)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.028106167787&{}:{}&-0.010735600801&{}:{}&-0.017370566986&,\\B^\prime&{}\approx{}&4.053678004005&{}:{}&3.505310785923&{}:{}&-6.558988789928&,\\C^\prime&{}\approx{}&0.665147500340&{}:{}&-0.665147500340&{}:{}&1.000000000000&. \end{alignedat} \]
7a (233)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.017370566986\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-6.558988789928\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.076231263082\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.618033988750&{}:{}&0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
7a (233)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.088335723635&{}:{}&-0.040692322547&{}:{}&-0.047643401087&. \end{alignedat} \]
7a (233)

Hiroyasu Kamo