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]

\(\mathbf{5c}\) \((312)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-2.564755078384&{}:{}&-14.259020313537&{}:{}&17.823775391922&,\\B^\prime&{}\approx{}&-0.613130530351&{}:{}&0.591246313100&{}:{}&1.021884217251&,\\C^\prime&{}\approx{}&-0.137704095259&{}:{}&-0.183605460346&{}:{}&1.321309555605&. \end{alignedat} \]
5c (312)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-7.129510156769\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.408753686900\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.091802730173\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \]
5c (312)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.442293769655&{}:{}&-0.278630327865&{}:{}&1.720924097520&. \end{alignedat} \]
5c (312)

Hiroyasu Kamo