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]

\(\mathbf{6b}\) \((321)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&15.038620480927&{}:{}&16.559681942832&{}:{}&-30.598302423759&,\\B^\prime&{}\approx{}&-0.006355829153&{}:{}&1.018099870087&{}:{}&-0.011744040934&,\\C^\prime&{}\approx{}&-0.550039664287&{}:{}&0.550039664287&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-30.598302423759\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.011744040934\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.016340775808\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.541196100146&{}:{}&-0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.024926963029&{}:{}&1.044197063812&{}:{}&-0.019270100783&. \end{alignedat} \]
6b (321)

Hiroyasu Kamo