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]

\(\mathbf{1c}\) \((112)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.612295904741&{}:{}&-1.550816381038&{}:{}&1.938520476297&,\\B^\prime&{}\approx{}&-0.967232496600&{}:{}&0.355178335600&{}:{}&1.612054161000&,\\C^\prime&{}\approx{}&-3.314755078384&{}:{}&-4.419673437846&{}:{}&8.734428516230&. \end{alignedat} \]
1c (112)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.775408190519\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.644821664400\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-2.209836718923\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \]
1c (112)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.805390790266&{}:{}&-1.328310188544&{}:{}&3.133700978809&. \end{alignedat} \]
1c (112)

Hiroyasu Kamo