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]

\(\mathbf{6c}\) \((330)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.481250000000&{}:{}&1.367187500000&{}:{}&-1.848437500000&,\\B^\prime&{}\approx{}&0.300000000000&{}:{}&1.303571428571&{}:{}&-0.603571428571&,\\C^\prime&{}\approx{}&0.300000000000&{}:{}&0.446428571429&{}:{}&0.253571428571&. \end{alignedat} \]
6c (330)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.437500000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.142857142857\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.142857142857\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
6c (330)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.533333333333&{}:{}&0.972222222222&{}:{}&-0.505555555556&. \end{alignedat} \]
6c (330)

Hiroyasu Kamo