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]

\(\mathbf{4a}\) \((211)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&2.000000000000&{}:{}&-0.425170068027&{}:{}&-0.574829931973&,\\B^\prime&{}\approx{}&2.240000000000&{}:{}&3.266666666667&{}:{}&-4.506666666667&,\\C^\prime&{}\approx{}&0.875000000000&{}:{}&-1.302083333333&{}:{}&1.427083333333&. \end{alignedat} \]
4a (211)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.714285714286\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-5.600000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-2.187500000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
4a (211)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.623188405797&{}:{}&-0.120772946860&{}:{}&-0.502415458937&. \end{alignedat} \]
4a (211)

Hiroyasu Kamo