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]

\(\mathbf{1b}\) \((103)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.937152698242&{}:{}&-0.101689070346&{}:{}&0.164536372104&,\\B^\prime&{}\approx{}&0.427958173665&{}:{}&-0.120409044417&{}:{}&0.692450870753&,\\C^\prime&{}\approx{}&1.260073510670&{}:{}&-1.260073510670&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.164536372104\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.692450870753\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}2.038841768588\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.618033988750&{}:{}&-0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.791217101774&{}:{}&-0.280216163150&{}:{}&0.488999061376&. \end{alignedat} \]
1b (103)

Hiroyasu Kamo