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]

\(\mathbf{4}\) \((200)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.982716049383&{}:{}&0.007348618460&{}:{}&0.009935332158&,\\B^\prime&{}\approx{}&0.625000000000&{}:{}&-0.882440476190&{}:{}&1.257440476190&,\\C^\prime&{}\approx{}&1.600000000000&{}:{}&2.380952380952&{}:{}&-2.980952380952&. \end{alignedat} \]
4 (200)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.022222222222\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.812500000000\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}7.200000000000\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.222222222222&{}:{}&0.330687830688&{}:{}&0.447089947090&. \end{alignedat} \]
4 (200)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.941176470588&{}:{}&0.022408963585&{}:{}&0.036414565826&. \end{alignedat} \]
4 (200)

Hiroyasu Kamo