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]

\(\mathbf{3c}\) \((132)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.535937500000&{}:{}&-1.318359375000&{}:{}&1.782421875000&,\\B^\prime&{}\approx{}&-11.200000000000&{}:{}&-10.333333333333&{}:{}&22.533333333333&,\\C^\prime&{}\approx{}&-0.311111111111&{}:{}&-0.462962962963&{}:{}&1.774074074074&. \end{alignedat} \]
3c (132)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.421875000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-5.333333333333\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.148148148148\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
3c (132)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.443564356436&{}:{}&-1.336633663366&{}:{}&2.780198019802&. \end{alignedat} \]
3c (132)

Hiroyasu Kamo