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]

\(\mathbf{2c}\) \((130)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.120312500000&{}:{}&0.341796875000&{}:{}&-0.462109375000&,\\B^\prime&{}\approx{}&10.800000000000&{}:{}&11.928571428571&{}:{}&-21.728571428571&,\\C^\prime&{}\approx{}&0.533333333333&{}:{}&0.793650793651&{}:{}&-0.326984126984&. \end{alignedat} \]
2c (130)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.109375000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}5.142857142857\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.253968253968\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
2c (130)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.159731543624&{}:{}&0.939597315436&{}:{}&-1.099328859060&. \end{alignedat} \]
2c (130)

Hiroyasu Kamo