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]

\(\mathbf{2c}\) \((130)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.056565265175&{}:{}&0.226261060701&{}:{}&-0.282826325877&,\\B^\prime&{}\approx{}&6.629510156769&{}:{}&5.419673437846&{}:{}&-11.049183594614&,\\C^\prime&{}\approx{}&0.483616248300&{}:{}&0.644821664400&{}:{}&-0.128437912700&. \end{alignedat} \]
2c (130)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.113130530351\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}4.419673437846\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.322410832200\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \]
2c (130)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.039077103195&{}:{}&0.654583929966&{}:{}&-0.693661033161&. \end{alignedat} \]
2c (130)

Hiroyasu Kamo