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]

\(\mathbf{7b}\) \((323)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.062500000000&{}:{}&5.859375000000&{}:{}&-7.921875000000&,\\B^\prime&{}\approx{}&-0.012152777778&{}:{}&1.036603009259&{}:{}&-0.024450231481&,\\C^\prime&{}\approx{}&-0.437500000000&{}:{}&0.651041666667&{}:{}&0.786458333333&. \end{alignedat} \]
7b (323)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-6.000000000000\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.018518518519\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-0.666666666667\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&. \end{alignedat} \]
7b (323)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.046052631579&{}:{}&1.110197368421&{}:{}&-0.064144736842&. \end{alignedat} \]
7b (323)

Hiroyasu Kamo