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]

\(\mathbf{3a}\) \((033)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.247797585933&{}:{}&0.264138361741&{}:{}&0.488064052326&,\\B^\prime&{}\approx{}&-4.496290132666&{}:{}&-2.811770718939&{}:{}&8.308060851606&,\\C^\prime&{}\approx{}&-0.013235329055&{}:{}&0.013235329055&{}:{}&1.000000000000&. \end{alignedat} \]
3a (033)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.488064052326\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}8.308060851606\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.024455699240\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
3a (033)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.020184590973&{}:{}&0.049671834969&{}:{}&0.970512756004&. \end{alignedat} \]
3a (033)

Hiroyasu Kamo