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]

\(\mathbf{7a}\) \((233)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.022222222222&{}:{}&-0.009448223734&{}:{}&-0.012773998488&,\\B^\prime&{}\approx{}&2.800000000000&{}:{}&3.833333333333&{}:{}&-5.633333333333&,\\C^\prime&{}\approx{}&0.700000000000&{}:{}&-1.041666666667&{}:{}&1.341666666667&. \end{alignedat} \]
7a (233)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.015873015873\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-7.000000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.750000000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
7a (233)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.072340425532&{}:{}&-0.035460992908&{}:{}&-0.036879432624&. \end{alignedat} \]
7a (233)

Hiroyasu Kamo