Derousseau's Generalization of the Malfatti circles

\(A=36\degree\), \(B=36\degree\), \(C=108\degree\).

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[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{1c}\) \((112)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.221231742082&{}:{}&-1.260073510670&{}:{}&2.038841768588&,\\B^\prime&{}\approx{}&-1.260073510670&{}:{}&0.221231742082&{}:{}&2.038841768588&,\\C^\prime&{}\approx{}&-7.679397834345&{}:{}&-7.679397834345&{}:{}&16.358795668690&. \end{alignedat} \]
1c (112)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.481305252753\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.481305252753\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-2.933268959588\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.618033988750&{}:{}&2.618033988750&{}:{}&-4.236067977500&. \end{alignedat} \]
1c (112)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-1.403979697400&{}:{}&-1.403979697400&{}:{}&3.807959394800&. \end{alignedat} \]
1c (112)

Hiroyasu Kamo