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]

\(\mathbf{4b}\) \((301)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-2.712500000000&{}:{}&-10.546875000000&{}:{}&14.259375000000&,\\B^\prime&{}\approx{}&0.243055555556&{}:{}&0.267939814815&{}:{}&0.489004629630&,\\C^\prime&{}\approx{}&0.021875000000&{}:{}&-0.032552083333&{}:{}&1.010677083333&. \end{alignedat} \]
4b (301)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}10.800000000000\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.370370370370\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.033333333333\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&. \end{alignedat} \]
4b (301)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.079545454545&{}:{}&-0.076704545455&{}:{}&0.997159090909&. \end{alignedat} \]
4b (301)

Hiroyasu Kamo