Derousseau's Generalization of the Malfatti circles

The Smallest Pythagorean Triangle

\(C=90\degree\).   \(a:b:c=3:4:5\).


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

\(\mathbf{6b}\) \((321)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.389140284973&{}:{}&9.556561139893&{}:{}&-11.945701424867&,\\B^\prime&{}\approx{}&-0.039240056597&{}:{}&1.104640150925&{}:{}&-0.065400094328&,\\C^\prime&{}\approx{}&-0.537910698151&{}:{}&0.717214264202&{}:{}&0.820696433950&. \end{alignedat} \]
6b (321)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-9.556561139893\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.052320075462\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-0.717214264202\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.750000000000&{}:{}&-1.000000000000&{}:{}&1.250000000000&. \end{alignedat} \]
6b (321)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.143510376500&{}:{}&1.239314196762&{}:{}&-0.095803820262&. \end{alignedat} \]
6b (321)

Hiroyasu Kamo