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]

\(\mathbf{7a}\) \((233)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.012093946541&{}:{}&-0.004246829266&{}:{}&-0.007847117275&,\\B^\prime&{}\approx{}&11.064825724938&{}:{}&10.380306311212&{}:{}&-20.445132036150&,\\C^\prime&{}\approx{}&0.554431429201&{}:{}&-0.554431429201&{}:{}&1.000000000000&. \end{alignedat} \]
7a (233)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.007847117275\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-20.445132036150\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.024455699240\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
7a (233)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.035767662910&{}:{}&-0.016653122231&{}:{}&-0.019114540678&. \end{alignedat} \]
7a (233)

Hiroyasu Kamo