Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{2}\) \((020)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.558260083544&{}:{}&0.645452460308&{}:{}&0.912807623235&,\\B^\prime&{}\approx{}&0.011401789184&{}:{}&0.972473645917&{}:{}&0.016124564899&,\\C^\prime&{}\approx{}&1.207106781187&{}:{}&1.207106781187&{}:{}&-1.414213562373&. \end{alignedat} \]
2 (020)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}2.203712543852\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.038928143267\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}4.121320343560\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.292893218813&{}:{}&0.292893218813&{}:{}&0.414213562373&. \end{alignedat} \]
2 (020)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.035883532499&{}:{}&0.906925509083&{}:{}&0.057190958418&. \end{alignedat} \]
2 (020)

Hiroyasu Kamo