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]

\(\mathbf{3c}\) \((132)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.477503149817&{}:{}&-0.845417662611&{}:{}&1.367914512795&,\\B^\prime&{}\approx{}&-17.789689572610&{}:{}&-9.994632805183&{}:{}&28.784322377793&,\\C^\prime&{}\approx{}&-0.287128803051&{}:{}&-0.287128803051&{}:{}&1.574257606102&. \end{alignedat} \]
3c (132)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.322920812428\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-6.795056767428\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.109673443616\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.618033988750&{}:{}&2.618033988750&{}:{}&-4.236067977500&. \end{alignedat} \]
3c (132)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.445681692658&{}:{}&-0.844311517102&{}:{}&2.289993209760&. \end{alignedat} \]
3c (132)

Hiroyasu Kamo