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]

\(\mathbf{5c}\) \((312)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-8.625000000000&{}:{}&-27.343750000000&{}:{}&36.968750000000&,\\B^\prime&{}\approx{}&-0.540000000000&{}:{}&0.453571428571&{}:{}&1.086428571429&,\\C^\prime&{}\approx{}&-0.166666666667&{}:{}&-0.248015873016&{}:{}&1.414682539683&. \end{alignedat} \]
5c (312)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-8.750000000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.257142857143\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.079365079365\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
5c (312)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.504672897196&{}:{}&-0.408878504673&{}:{}&1.913551401869&. \end{alignedat} \]
5c (312)

Hiroyasu Kamo