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]

\(\mathbf{1c}\) \((112)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.382683432365&{}:{}&-1.630986313698&{}:{}&3.013669746063&,\\B^\prime&{}\approx{}&-1.630986313698&{}:{}&-0.382683432365&{}:{}&3.013669746063&,\\C^\prime&{}\approx{}&-32.549704743153&{}:{}&-32.549704743153&{}:{}&66.099409486307&. \end{alignedat} \]
1c (112)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.248302881333\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.248302881333\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-4.955397483337\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \]
1c (112)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-2.443405087842&{}:{}&-2.443405087842&{}:{}&5.886810175683&. \end{alignedat} \]
1c (112)

Hiroyasu Kamo