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]

\(\mathbf{1c}\) \((112)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.398437500000&{}:{}&-1.708984375000&{}:{}&2.310546875000&,\\B^\prime&{}\approx{}&-0.960000000000&{}:{}&0.028571428571&{}:{}&1.931428571429&,\\C^\prime&{}\approx{}&-6.000000000000&{}:{}&-8.928571428571&{}:{}&15.928571428571&. \end{alignedat} \]
1c (112)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.546875000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.457142857143\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-2.857142857143\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
1c (112)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-1.032258064516&{}:{}&-1.881720430108&{}:{}&3.913978494624&. \end{alignedat} \]
1c (112)

Hiroyasu Kamo