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]

\(\mathbf{3c}\) \((132)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.693434734825&{}:{}&-1.226261060701&{}:{}&1.532826325877&,\\B^\prime&{}\approx{}&-7.129510156769&{}:{}&-3.753006771179&{}:{}&11.882516927948&,\\C^\prime&{}\approx{}&-0.233616248300&{}:{}&-0.311488331067&{}:{}&1.545104579367&. \end{alignedat} \]
3c (132)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.613130530351\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-4.753006771179\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.155744165533\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \]
3c (132)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.301656096168&{}:{}&-0.957689085290&{}:{}&2.259345181458&. \end{alignedat} \]
3c (132)

Hiroyasu Kamo