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]

\(\mathbf{0c}\) \((110)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.923879532511&{}:{}&1.089790213552&{}:{}&-2.013669746063&,\\B^\prime&{}\approx{}&1.089790213552&{}:{}&1.923879532511&{}:{}&-2.013669746063&,\\C^\prime&{}\approx{}&32.809596275628&{}:{}&32.809596275628&{}:{}&-64.619192551255&. \end{alignedat} \]
0c (110)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.165910681040\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.165910681040\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}4.994963613233\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \]
0c (110)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&2.481806171257&{}:{}&2.481806171257&{}:{}&-3.963612342513&. \end{alignedat} \]
0c (110)

Hiroyasu Kamo