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]

\(\mathbf{1}\) \((002)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.066666666667&{}:{}&0.453514739229&{}:{}&0.613151927438&,\\B^\prime&{}\approx{}&0.364583333333&{}:{}&-0.098090277778&{}:{}&0.733506944444&,\\C^\prime&{}\approx{}&0.025925925926&{}:{}&0.038580246914&{}:{}&0.935493827160&. \end{alignedat} \]
1 (002)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.371428571429\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.640625000000\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.116666666667\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&. \end{alignedat} \]
1 (002)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.080459770115&{}:{}&0.122605363985&{}:{}&0.796934865900&. \end{alignedat} \]
1 (002)

Hiroyasu Kamo