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]

\(\mathbf{7}\) \((222)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.071882550435&{}:{}&0.409422702318&{}:{}&0.662459848116&,\\B^\prime&{}\approx{}&0.409422702318&{}:{}&-0.071882550435&{}:{}&0.662459848116&,\\C^\prime&{}\approx{}&2.495187611587&{}:{}&2.495187611587&{}:{}&-3.990375223174&. \end{alignedat} \]
7 (222)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.481305252753\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.481305252753\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}9.027673587030\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.276393202250&{}:{}&0.276393202250&{}:{}&0.447213595500&. \end{alignedat} \]
7 (222)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.456180656796&{}:{}&0.456180656796&{}:{}&0.087638686407&. \end{alignedat} \]
7 (222)

Hiroyasu Kamo