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]

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.865858935109&{}:{}&0.655202526796&{}:{}&1.210656408313&,\\B^\prime&{}\approx{}&-0.160638130892&{}:{}&0.863817568348&{}:{}&0.296820562545&,\\C^\prime&{}\approx{}&-0.370459237183&{}:{}&0.370459237183&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.210656408313\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.296820562545\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.684519413727\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.390648057027&{}:{}&0.647474008384&{}:{}&0.743174048643&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo