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]

\(\mathbf{1a}\) \((013)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.246727081811&{}:{}&0.437792331916&{}:{}&0.808934749895&,\\B^\prime&{}\approx{}&-0.107334967498&{}:{}&0.909005808310&{}:{}&0.198329159188&,\\C^\prime&{}\approx{}&-0.823192531266&{}:{}&0.823192531266&{}:{}&1.000000000000&. \end{alignedat} \]
1a (013)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.808934749895\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.198329159188\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}1.521061461906\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
1a (013)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.297327717849&{}:{}&0.731687521071&{}:{}&0.565640196777&. \end{alignedat} \]
1a (013)

Hiroyasu Kamo