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]

\(\mathbf{6b}\) \((321)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&5.812500000000&{}:{}&13.671875000000&{}:{}&-18.484375000000&,\\B^\prime&{}\approx{}&-0.020833333333&{}:{}&1.062748015873&{}:{}&-0.041914682540&,\\C^\prime&{}\approx{}&-0.421875000000&{}:{}&0.627790178571&{}:{}&0.794084821429&. \end{alignedat} \]
6b (321)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-14.000000000000\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.031746031746\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-0.642857142857\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.656250000000&{}:{}&-0.976562500000&{}:{}&1.320312500000&. \end{alignedat} \]
6b (321)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.078488372093&{}:{}&1.144622093023&{}:{}&-0.066133720930&. \end{alignedat} \]
6b (321)

Hiroyasu Kamo