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]

\(\mathbf{5a}\) \((213)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.259259259259&{}:{}&-0.110229276896&{}:{}&-0.149029982363&,\\B^\prime&{}\approx{}&2.160000000000&{}:{}&3.185714285714&{}:{}&-4.345714285714&,\\C^\prime&{}\approx{}&1.500000000000&{}:{}&-2.232142857143&{}:{}&1.732142857143&. \end{alignedat} \]
5a (213)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.185185185185\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-5.400000000000\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-3.750000000000\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.400000000000&{}:{}&0.595238095238&{}:{}&0.804761904762&. \end{alignedat} \]
5a (213)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.521126760563&{}:{}&-0.050301810865&{}:{}&-0.470824949698&. \end{alignedat} \]
5a (213)

Hiroyasu Kamo