Derousseau's Generalization of the Malfatti circles

\(A=22.5\degree\), \(B=22.5\degree\), \(C=135\degree\).

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[Guy]
[Lob & Richmond]

\(\mathbf{6c}\) \((330)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.923879532511&{}:{}&1.089790213552&{}:{}&-2.013669746063&,\\B^\prime&{}\approx{}&1.089790213552&{}:{}&1.923879532511&{}:{}&-2.013669746063&,\\C^\prime&{}\approx{}&0.472553645310&{}:{}&0.472553645310&{}:{}&0.054892709380&. \end{alignedat} \]
6cā€‚(330)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.165910681040\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.165910681040\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.071942008789\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \]
6cā€‚(330)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.081837671059&{}:{}&1.081837671059&{}:{}&-1.163675342118&. \end{alignedat} \]
6cā€‚(330)

Hiroyasu Kamo