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]

\(\mathbf{3}\) \((022)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.382716049383&{}:{}&0.587889476778&{}:{}&0.794826572604&,\\B^\prime&{}\approx{}&0.031250000000&{}:{}&0.905877976190&{}:{}&0.062872023810&,\\C^\prime&{}\approx{}&0.500000000000&{}:{}&0.744047619048&{}:{}&-0.244047619048&. \end{alignedat} \]
3 (022)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.777777777778\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.140625000000\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}2.250000000000\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&. \end{alignedat} \]
3 (022)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.020408163265&{}:{}&0.777453838678&{}:{}&0.202137998056&. \end{alignedat} \]
3 (022)

Hiroyasu Kamo