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]

\(\mathbf{6c}\) \((330)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.233616248300&{}:{}&0.934464993201&{}:{}&-1.168081241501&,\\B^\prime&{}\approx{}&0.275408190519&{}:{}&1.183605460346&{}:{}&-0.459013650865&,\\C^\prime&{}\approx{}&0.306565265175&{}:{}&0.408753686900&{}:{}&0.284681047924&. \end{alignedat} \]
6c (330)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.467232496600\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.183605460346\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.204376843450\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \]
6c (330)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.504617259636&{}:{}&0.832252187871&{}:{}&-0.336869447506&. \end{alignedat} \]
6c (330)

Hiroyasu Kamo