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]

\(\mathbf{2a}\) \((031)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.241791662387&{}:{}&0.266247361627&{}:{}&0.491960975985&,\\B^\prime&{}\approx{}&-9.991146350560&{}:{}&-7.470084888655&{}:{}&18.461231239215&,\\C^\prime&{}\approx{}&-0.008843564140&{}:{}&0.008843564140&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.491960975985\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}18.461231239215\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.016340775808\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.020517324001&{}:{}&0.034006143825&{}:{}&0.986511180176&. \end{alignedat} \]
2a (031)

Hiroyasu Kamo