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]

\(\mathbf{6}\) \((220)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.666666666667&{}:{}&0.141723356009&{}:{}&0.191609977324&,\\B^\prime&{}\approx{}&0.291666666667&{}:{}&0.121527777778&{}:{}&0.586805555556&,\\C^\prime&{}\approx{}&2.074074074074&{}:{}&3.086419753086&{}:{}&-4.160493827160&. \end{alignedat} \]
6 (220)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.428571428571\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.312500000000\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}9.333333333333\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&. \end{alignedat} \]
6 (220)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.612021857923&{}:{}&0.364298724954&{}:{}&0.023679417122&. \end{alignedat} \]
6 (220)

Hiroyasu Kamo