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]

\(\mathbf{2a}\) \((031)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.158475478364&{}:{}&0.374010898505&{}:{}&0.467513623131&,\\B^\prime&{}\approx{}&-2.597262605646&{}:{}&-0.731508403764&{}:{}&4.328771009409&,\\C^\prime&{}\approx{}&-0.032507527261&{}:{}&0.043343369682&{}:{}&0.989164157580&. \end{alignedat} \]
2a (031)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.561016347758\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}5.194525211291\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.065015054523\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.500000000000&{}:{}&0.666666666667&{}:{}&0.833333333333&. \end{alignedat} \]
2a (031)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.084146438277&{}:{}&0.151071695632&{}:{}&0.933074742645&. \end{alignedat} \]
2a (031)

Hiroyasu Kamo