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]

\(\mathbf{0b}\) \((101)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.863817568348&{}:{}&-0.160638130892&{}:{}&0.296820562545&,\\B^\prime&{}\approx{}&0.655202526796&{}:{}&-0.865858935109&{}:{}&1.210656408313&,\\C^\prime&{}\approx{}&0.370459237183&{}:{}&-0.370459237183&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.296820562545\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}1.210656408313\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.684519413727\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.541196100146&{}:{}&-0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.647474008384&{}:{}&-0.390648057027&{}:{}&0.743174048643&. \end{alignedat} \]
0b (101)

Hiroyasu Kamo