Derousseau's Generalization of the Malfatti circles

\(A=45\degree\), \(B=45\degree\), \(C=90\degree\).


[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{5c}\) \((312)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-3.054865846209&{}:{}&-9.789312119522&{}:{}&13.844177965731&,\\B^\prime&{}\approx{}&-0.867542129971&{}:{}&0.640652283836&{}:{}&1.226889846135&,\\C^\prime&{}\approx{}&-0.207106781187&{}:{}&-0.207106781187&{}:{}&1.414213562373&. \end{alignedat} \]
5c (312)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-5.734446273312\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.508194413807\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.121320343560\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.707106781187&{}:{}&1.707106781187&{}:{}&-2.414213562373&. \end{alignedat} \]
5c (312)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.651803220840&{}:{}&-0.291005820742&{}:{}&1.942809041582&. \end{alignedat} \]
5c (312)

Hiroyasu Kamo