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]

\(\mathbf{5a}\) \((213)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.396802246667&{}:{}&-0.151564971415&{}:{}&-0.245237275253&,\\B^\prime&{}\approx{}&2.719723059095&{}:{}&2.680881290508&{}:{}&-4.400604349603&,\\C^\prime&{}\approx{}&1.878107499420&{}:{}&-1.878107499420&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.245237275253\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-4.400604349603\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-3.038841768588\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.618033988750&{}:{}&0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.824968519586&{}:{}&-0.068234650416&{}:{}&-0.756733869169&. \end{alignedat} \]
5a (213)

Hiroyasu Kamo