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]

\(\mathbf{2b}\) \((121)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&6.704718023924&{}:{}&6.729173723164&{}:{}&-12.433891747089&,\\B^\prime&{}\approx{}&-0.395310994322&{}:{}&2.125750467584&{}:{}&-0.730439473262&,\\C^\prime&{}\approx{}&-0.911655337330&{}:{}&0.911655337330&{}:{}&1.000000000000&. \end{alignedat} \]
2b (121)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-12.433891747089\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.730439473262\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.684519413727\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.541196100146&{}:{}&-0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
2b (121)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.046834520438&{}:{}&1.961910428851&{}:{}&-0.915075908413&. \end{alignedat} \]
2b (121)

Hiroyasu Kamo