Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{4b}\) \((301)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-3.863703305156&{}:{}&-6.643942271314&{}:{}&11.507645576470&,\\B^\prime&{}\approx{}&0.280861170610&{}:{}&0.232673012021&{}:{}&0.486465817369&,\\C^\prime&{}\approx{}&0.016062719530&{}:{}&-0.016062719530&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}11.507645576470\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.486465817369\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.027821446333\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.577350269190&{}:{}&-0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.060118012533&{}:{}&-0.038494686889&{}:{}&0.978376674356&. \end{alignedat} \]
4b (301)

Hiroyasu Kamo