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]

\(\mathbf{2}\) \((020)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.333333333333&{}:{}&0.566893424036&{}:{}&0.766439909297&,\\B^\prime&{}\approx{}&0.008101851852&{}:{}&0.975597993827&{}:{}&0.016300154321&,\\C^\prime&{}\approx{}&1.166666666667&{}:{}&1.736111111111&{}:{}&-1.902777777778&. \end{alignedat} \]
2 (020)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.714285714286\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.036458333333\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}5.250000000000\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&. \end{alignedat} \]
2 (020)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.024054982818&{}:{}&0.916380297824&{}:{}&0.059564719359&. \end{alignedat} \]
2 (020)

Hiroyasu Kamo