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]

\(\mathbf{1b}\) \((103)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.909005808310&{}:{}&-0.107334967498&{}:{}&0.198329159188&,\\B^\prime&{}\approx{}&0.437792331916&{}:{}&-0.246727081811&{}:{}&0.808934749895&,\\C^\prime&{}\approx{}&0.823192531266&{}:{}&-0.823192531266&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.198329159188\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.808934749895\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}1.521061461906\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.541196100146&{}:{}&-0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.731687521071&{}:{}&-0.297327717849&{}:{}&0.565640196777&. \end{alignedat} \]
1b (103)

Hiroyasu Kamo