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]

\(\mathbf{7c}\) \((332)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.175000000000&{}:{}&-2.343750000000&{}:{}&3.168750000000&,\\B^\prime&{}\approx{}&-0.700000000000&{}:{}&0.291666666667&{}:{}&1.408333333333&,\\C^\prime&{}\approx{}&-0.077777777778&{}:{}&-0.115740740741&{}:{}&1.193518518519&. \end{alignedat} \]
7c (332)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.750000000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.333333333333\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.037037037037\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
7c (332)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.254545454545&{}:{}&-0.340909090909&{}:{}&1.595454545455&. \end{alignedat} \]
7c (332)

Hiroyasu Kamo