Derousseau's Generalization of the Malfatti circles

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

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[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{5}\) \((202)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.977945244486&{}:{}&0.007744600231&{}:{}&0.014310155282&,\\B^\prime&{}\approx{}&0.537710817439&{}:{}&-0.531270854722&{}:{}&0.993560037284&,\\C^\prime&{}\approx{}&2.630986313698&{}:{}&2.630986313698&{}:{}&-4.261972627396&. \end{alignedat} \]
5 (202)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.029799355745\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.068981672161\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}10.123401438481\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&. \end{alignedat} \]
5 (202)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.937018949093&{}:{}&0.009089605290&{}:{}&0.053891445616&. \end{alignedat} \]
5 (202)

Hiroyasu Kamo