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]

\(\mathbf{0}\) \((000)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.382683432365&{}:{}&0.216772751325&{}:{}&0.400543816310&,\\B^\prime&{}\approx{}&0.216772751325&{}:{}&0.382683432365&{}:{}&0.400543816310&,\\C^\prime&{}\approx{}&0.093996764303&{}:{}&0.093996764303&{}:{}&0.812006471395&. \end{alignedat} \]
0 (000)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.834089318960\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.834089318960\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.361676901928\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&. \end{alignedat} \]
0 (000)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.215190892271&{}:{}&0.215190892271&{}:{}&0.569618215458&. \end{alignedat} \]
0 (000)

Hiroyasu Kamo