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]

\(\mathbf{3}\) \((022)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.531270854722&{}:{}&0.537710817439&{}:{}&0.993560037284&,\\B^\prime&{}\approx{}&0.007744600231&{}:{}&0.977945244486&{}:{}&0.014310155282&,\\C^\prime&{}\approx{}&2.630986313698&{}:{}&2.630986313698&{}:{}&-4.261972627396&. \end{alignedat} \]
3 (022)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}2.068981672161\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.029799355745\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}10.123401438481\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&. \end{alignedat} \]
3 (022)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.009089605290&{}:{}&0.937018949093&{}:{}&0.053891445616&. \end{alignedat} \]
3 (022)

Hiroyasu Kamo