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]

\(\mathbf{5b}\) \((303)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.037500000000&{}:{}&-2.734375000000&{}:{}&3.696875000000&,\\B^\prime&{}\approx{}&0.234375000000&{}:{}&0.294084821429&{}:{}&0.471540178571&,\\C^\prime&{}\approx{}&0.037500000000&{}:{}&-0.055803571429&{}:{}&1.018303571429&. \end{alignedat} \]
5b (303)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}2.800000000000\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.357142857143\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.057142857143\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&. \end{alignedat} \]
5b (303)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.125000000000&{}:{}&-0.072916666667&{}:{}&0.947916666667&. \end{alignedat} \]
5b (303)

Hiroyasu Kamo