Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{2a}\) \((031)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.232673012021&{}:{}&0.280861170610&{}:{}&0.486465817369&,\\B^\prime&{}\approx{}&-6.643942271314&{}:{}&-3.863703305156&{}:{}&11.507645576470&,\\C^\prime&{}\approx{}&-0.016062719530&{}:{}&0.016062719530&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.486465817369\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}11.507645576470\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.027821446333\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.577350269190&{}:{}&0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.038494686889&{}:{}&0.060118012533&{}:{}&0.978376674356&. \end{alignedat} \]
2a (031)

Hiroyasu Kamo