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]

\(\mathbf{6}\) \((220)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.667552905630&{}:{}&0.147754264164&{}:{}&0.184692830205&,\\B^\prime&{}\approx{}&0.281999757518&{}:{}&0.248000646617&{}:{}&0.469999595864&,\\C^\prime&{}\approx{}&1.476569900005&{}:{}&1.968759866674&{}:{}&-2.445329766679&. \end{alignedat} \]
6 (220)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.443262792493\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.127999030074\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}5.906279600021\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.250000000000&{}:{}&0.333333333333&{}:{}&0.416666666667&. \end{alignedat} \]
6 (220)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.588856682171&{}:{}&0.381640981690&{}:{}&0.029502336139&. \end{alignedat} \]
6 (220)

Hiroyasu Kamo