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]

\(\mathbf{4c}\) \((310)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&10.281250000000&{}:{}&26.367187500000&{}:{}&-35.648437500000&,\\B^\prime&{}\approx{}&0.140000000000&{}:{}&1.141666666667&{}:{}&-0.281666666667&,\\C^\prime&{}\approx{}&0.388888888889&{}:{}&0.578703703704&{}:{}&0.032407407407&. \end{alignedat} \]
4c (310)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}8.437500000000\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.066666666667\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.185185185185\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.100000000000&{}:{}&3.125000000000&{}:{}&-4.225000000000&. \end{alignedat} \]
4c (310)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.408759124088&{}:{}&1.231751824818&{}:{}&-0.640510948905&. \end{alignedat} \]
4c (310)

Hiroyasu Kamo