Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{5a}\) \((213)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.443016443066&{}:{}&-0.162155272456&{}:{}&-0.280861170610&,\\B^\prime&{}\approx{}&3.835881858823&{}:{}&3.808060412490&{}:{}&-6.643942271314&,\\C^\prime&{}\approx{}&1.605171715523&{}:{}&-1.605171715523&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.280861170610\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-6.643942271314\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-2.780238966158\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.577350269190&{}:{}&0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.878238345509&{}:{}&-0.050840841584&{}:{}&-0.827397503925&. \end{alignedat} \]
5a (213)

Hiroyasu Kamo