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]

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.777777777778&{}:{}&0.755857898715&{}:{}&1.021919879063&,\\B^\prime&{}\approx{}&-0.140000000000&{}:{}&0.858333333333&{}:{}&0.281666666667&,\\C^\prime&{}\approx{}&-0.218750000000&{}:{}&0.325520833333&{}:{}&0.893229166667&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.269841269841\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.350000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.546875000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.301435406699&{}:{}&0.637958532695&{}:{}&0.663476874003&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo