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]

\(\mathbf{1a}\) \((013)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.037037037037&{}:{}&0.440917107584&{}:{}&0.596119929453&,\\B^\prime&{}\approx{}&-0.060000000000&{}:{}&0.939285714286&{}:{}&0.120714285714&,\\C^\prime&{}\approx{}&-0.843750000000&{}:{}&1.255580357143&{}:{}&0.588169642857&. \end{alignedat} \]
1a (013)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.740740740741\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.150000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}2.109375000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
1a (013)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.167701863354&{}:{}&0.798580301686&{}:{}&0.369121561668&. \end{alignedat} \]
1a (013)

Hiroyasu Kamo