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]

\(\mathbf{4a}\) \((211)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&2.475319763287&{}:{}&-0.563522005301&{}:{}&-0.911797757986&,\\B^\prime&{}\approx{}&2.817610026505&{}:{}&2.741378763423&{}:{}&-4.558988789928&,\\C^\prime&{}\approx{}&0.956943567841&{}:{}&-0.956943567841&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.911797757986\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-4.558988789928\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.548367218082\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.618033988750&{}:{}&0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.943587463614&{}:{}&-0.137667555613&{}:{}&-0.805919908001&. \end{alignedat} \]
4a (211)

Hiroyasu Kamo