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]

\(\mathbf{7c}\) \((332)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.382683432365&{}:{}&-1.630986313698&{}:{}&3.013669746063&,\\B^\prime&{}\approx{}&-1.630986313698&{}:{}&-0.382683432365&{}:{}&3.013669746063&,\\C^\prime&{}\approx{}&-0.212662112836&{}:{}&-0.212662112836&{}:{}&1.425324225672&. \end{alignedat} \]
7c (332)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.248302881333\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.248302881333\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.032375878892\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \]
7c (332)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.634051832675&{}:{}&-0.634051832675&{}:{}&2.268103665351&. \end{alignedat} \]
7c (332)

Hiroyasu Kamo