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]

\(\mathbf{5}\) \((202)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.933333333333&{}:{}&0.028344671202&{}:{}&0.038321995465&,\\B^\prime&{}\approx{}&0.648148148148&{}:{}&-0.952160493827&{}:{}&1.304012345679&,\\C^\prime&{}\approx{}&0.933333333333&{}:{}&1.388888888889&{}:{}&-1.322222222222&. \end{alignedat} \]
5 (202)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.085714285714\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.916666666667\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}4.200000000000\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&. \end{alignedat} \]
5 (202)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.848484848485&{}:{}&0.020202020202&{}:{}&0.131313131313&. \end{alignedat} \]
5 (202)

Hiroyasu Kamo