Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{6b}\) \((321)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&8.595754112725&{}:{}&10.375993078883&{}:{}&-17.971747191608&,\\B^\prime&{}\approx{}&-0.012911978179&{}:{}&1.035276180410&{}:{}&-0.022364202232&,\\C^\prime&{}\approx{}&-0.593412988719&{}:{}&0.593412988719&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-17.971747191608\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.022364202232\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.027821446333\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.577350269190&{}:{}&-0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.049840461676&{}:{}&1.084129032472&{}:{}&-0.034288570796&. \end{alignedat} \]
6b (321)

Hiroyasu Kamo