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]

\(\mathbf{5b}\) \((303)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.112723202827&{}:{}&-1.435644015255&{}:{}&2.322920812428&,\\B^\prime&{}\approx{}&0.287128803051&{}:{}&0.248287034463&{}:{}&0.464584162486&,\\C^\prime&{}\approx{}&0.047113511590&{}:{}&-0.047113511590&{}:{}&1.000000000000&. \end{alignedat} \]
5b (303)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}2.322920812428\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.464584162486\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.076231263082\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.618033988750&{}:{}&-0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
5b (303)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.153847488979&{}:{}&-0.054486376717&{}:{}&0.900638887737&. \end{alignedat} \]
5b (303)

Hiroyasu Kamo