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]

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-1.048631302823&{}:{}&0.910502801255&{}:{}&1.138128501568&,\\B^\prime&{}\approx{}&-0.183049043273&{}:{}&0.877967304485&{}:{}&0.305081738788&,\\C^\prime&{}\approx{}&-0.239614308448&{}:{}&0.319485744597&{}:{}&0.920128563851&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.365754201882\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.366098086545\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.479228616896\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.500000000000&{}:{}&0.666666666667&{}:{}&0.833333333333&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.370663725296&{}:{}&0.665468421915&{}:{}&0.705195303382&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo