Derousseau's Generalization of the Malfatti circles

Ajima's example

不朽算法 十四 (Fukyū Sanpō §14)

\(a=252\),  \(b=375\),  \(c=507\).  \(a:b:c=84:125:169\).


[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{6a}\) \((231)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.051851851852&{}:{}&-0.022045855379&{}:{}&-0.029805996473&,\\B^\prime&{}\approx{}&4.800000000000&{}:{}&5.857142857143&{}:{}&-9.657142857143&,\\C^\prime&{}\approx{}&0.675000000000&{}:{}&-1.004464285714&{}:{}&1.329464285714&. \end{alignedat} \]
6a (231)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.037037037037\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-12.000000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.687500000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
6a (231)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.122077922078&{}:{}&-0.083487940631&{}:{}&-0.038589981447&. \end{alignedat} \]
6a (231)

Hiroyasu Kamo