Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{6a}\) \((231)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.035276180410&{}:{}&-0.012911978179&{}:{}&-0.022364202232&,\\B^\prime&{}\approx{}&10.375993078883&{}:{}&8.595754112725&{}:{}&-17.971747191608&,\\C^\prime&{}\approx{}&0.593412988719&{}:{}&-0.593412988719&{}:{}&1.000000000000&. \end{alignedat} \]
6a (231)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.022364202232\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-17.971747191608\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.027821446333\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.577350269190&{}:{}&0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
6a (231)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.084129032472&{}:{}&-0.049840461676&{}:{}&-0.034288570796&. \end{alignedat} \]
6a (231)

Hiroyasu Kamo