Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{7}\) \((222)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.207106781187&{}:{}&0.500000000000&{}:{}&0.707106781187&,\\B^\prime&{}\approx{}&0.500000000000&{}:{}&-0.207106781187&{}:{}&0.707106781187&,\\C^\prime&{}\approx{}&1.558260083544&{}:{}&1.558260083544&{}:{}&-2.116520167087&. \end{alignedat} \]
7 (222)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.707106781187\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.707106781187\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}5.320232710939\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.292893218813&{}:{}&0.292893218813&{}:{}&0.414213562373&. \end{alignedat} \]
7 (222)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.422378967344&{}:{}&0.422378967344&{}:{}&0.155242065312&. \end{alignedat} \]
7 (222)

Hiroyasu Kamo