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]

\(\mathbf{2a}\) \((031)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.170370370370&{}:{}&0.352733686067&{}:{}&0.476895943563&,\\B^\prime&{}\approx{}&-2.700000000000&{}:{}&-1.732142857143&{}:{}&5.432142857143&,\\C^\prime&{}\approx{}&-0.018750000000&{}:{}&0.027901785714&{}:{}&0.990848214286&. \end{alignedat} \]
2a (031)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.592592592593\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}6.750000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.046875000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
2a (031)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.047787610619&{}:{}&0.101137800253&{}:{}&0.946649810367&. \end{alignedat} \]
2a (031)

Hiroyasu Kamo