Derousseau's Generalization of the Malfatti circles

\(A=30\degree\), \(B=30\degree\), \(C=120\degree\).


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

\(\mathbf{3b}\) \((123)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.808060412490&{}:{}&3.835881858823&{}:{}&-6.643942271314&,\\B^\prime&{}\approx{}&-0.162155272456&{}:{}&1.443016443066&{}:{}&-0.280861170610&,\\C^\prime&{}\approx{}&-1.605171715523&{}:{}&1.605171715523&{}:{}&1.000000000000&. \end{alignedat} \]
3b (123)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-6.643942271314\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.280861170610\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-2.780238966158\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.577350269190&{}:{}&-0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
3b (123)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.050840841584&{}:{}&1.878238345509&{}:{}&-0.827397503925&. \end{alignedat} \]
3b (123)

Hiroyasu Kamo