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]

\(\mathbf{0b}\) \((101)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.896875000000&{}:{}&-0.292968750000&{}:{}&0.396093750000&,\\B^\prime&{}\approx{}&0.972222222222&{}:{}&-1.928240740741&{}:{}&1.956018518519&,\\C^\prime&{}\approx{}&0.350000000000&{}:{}&-0.520833333333&{}:{}&1.170833333333&. \end{alignedat} \]
0b (101)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.300000000000\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}1.481481481481\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.533333333333\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&. \end{alignedat} \]
0b (101)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.700000000000&{}:{}&-0.675000000000&{}:{}&0.975000000000&. \end{alignedat} \]
0b (101)

Hiroyasu Kamo