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]

\(\mathbf{2b}\) \((121)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.578480113194&{}:{}&2.313920452774&{}:{}&-2.892400565968&,\\B^\prime&{}\approx{}&-0.944570142487&{}:{}&3.518853713298&{}:{}&-1.574283570811&,\\C^\prime&{}\approx{}&-0.848570869931&{}:{}&1.131427826575&{}:{}&0.717143043356&. \end{alignedat} \]
2b (121)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-2.313920452774\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-1.259426856649\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.131427826575\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.750000000000&{}:{}&-1.000000000000&{}:{}&1.250000000000&. \end{alignedat} \]
2b (121)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.267036670875&{}:{}&2.306051627355&{}:{}&-1.039014956480&. \end{alignedat} \]
2b (121)

Hiroyasu Kamo