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]

\(\mathbf{2}\) \((020)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.373016509412&{}:{}&0.610229559739&{}:{}&0.762786949673&,\\B^\prime&{}\approx{}&0.011715049997&{}:{}&0.968759866674&{}:{}&0.019525083329&,\\C^\prime&{}\approx{}&0.936000484963&{}:{}&1.248000646617&{}:{}&-1.184001131580&. \end{alignedat} \]
2 (020)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.830688679216\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.046860199990\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}3.744001939852\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.250000000000&{}:{}&0.333333333333&{}:{}&0.416666666667&. \end{alignedat} \]
2 (020)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.036345867083&{}:{}&0.894505378899&{}:{}&0.069148754018&. \end{alignedat} \]
2 (020)

Hiroyasu Kamo