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]

\(\mathbf{3a}\) \((033)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.200000000000&{}:{}&0.340136054422&{}:{}&0.459863945578&,\\B^\prime&{}\approx{}&-0.700000000000&{}:{}&0.291666666667&{}:{}&1.408333333333&,\\C^\prime&{}\approx{}&-0.043750000000&{}:{}&0.065104166667&{}:{}&0.978645833333&. \end{alignedat} \]
3a (033)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.571428571429\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}1.750000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.109375000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
3a (033)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.042424242424&{}:{}&0.202020202020&{}:{}&0.840404040404&. \end{alignedat} \]
3a (033)

Hiroyasu Kamo