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]

\(\mathbf{2b}\) \((121)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&2.203125000000&{}:{}&3.417968750000&{}:{}&-4.621093750000&,\\B^\prime&{}\approx{}&-0.750000000000&{}:{}&3.258928571429&{}:{}&-1.508928571429&,\\C^\prime&{}\approx{}&-0.750000000000&{}:{}&1.116071428571&{}:{}&0.633928571429&. \end{alignedat} \]
2b (121)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-3.500000000000\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-1.142857142857\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.142857142857\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&. \end{alignedat} \]
2b (121)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.166666666667&{}:{}&2.430555555556&{}:{}&-1.263888888889&. \end{alignedat} \]
2b (121)

Hiroyasu Kamo