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]

\(\mathbf{7c}\) \((332)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.516383751700&{}:{}&-1.934464993201&{}:{}&2.418081241501&,\\B^\prime&{}\approx{}&-0.775408190519&{}:{}&0.483061206321&{}:{}&1.292346984198&,\\C^\prime&{}\approx{}&-0.056565265175&{}:{}&-0.075420353567&{}:{}&1.131985618742&. \end{alignedat} \]
7c (332)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.967232496600\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.516938793679\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.037710176784\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \]
7c (332)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.189496231731&{}:{}&-0.229793494234&{}:{}&1.419289725966&. \end{alignedat} \]
7c (332)

Hiroyasu Kamo