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]

\(\mathbf{0c}\) \((110)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.257812500000&{}:{}&0.732421875000&{}:{}&-0.990234375000&,\\B^\prime&{}\approx{}&0.560000000000&{}:{}&1.566666666667&{}:{}&-1.126666666667&,\\C^\prime&{}\approx{}&6.222222222222&{}:{}&9.259259259259&{}:{}&-14.481481481481&. \end{alignedat} \]
0c (110)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.234375000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.266666666667\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}2.962962962963\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
0c (110)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.294797687861&{}:{}&1.734104046243&{}:{}&-2.028901734104&. \end{alignedat} \]
0c (110)

Hiroyasu Kamo