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]

\(\mathbf{1b}\) \((103)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.939843750000&{}:{}&-0.170898437500&{}:{}&0.231054687500&,\\B^\prime&{}\approx{}&0.416666666667&{}:{}&-0.254960317460&{}:{}&0.838293650794&,\\C^\prime&{}\approx{}&1.350000000000&{}:{}&-2.008928571429&{}:{}&1.658928571429&. \end{alignedat} \]
1b (103)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.175000000000\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.634920634921\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}2.057142857143\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&. \end{alignedat} \]
1b (103)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.794117647059&{}:{}&-0.463235294118&{}:{}&0.669117647059&. \end{alignedat} \]
1b (103)

Hiroyasu Kamo