Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{1c}\) \((112)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.500000000000&{}:{}&-1.207106781187&{}:{}&1.707106781187&,\\B^\prime&{}\approx{}&-1.207106781187&{}:{}&0.500000000000&{}:{}&1.707106781187&,\\C^\prime&{}\approx{}&-3.761972627396&{}:{}&-3.761972627396&{}:{}&8.523945254791&. \end{alignedat} \]
1c (112)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.707106781187\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.707106781187\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-2.203712543852\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.707106781187&{}:{}&1.707106781187&{}:{}&-2.414213562373&. \end{alignedat} \]
1c (112)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-1.019713031423&{}:{}&-1.019713031423&{}:{}&3.039426062845&. \end{alignedat} \]
1c (112)

Hiroyasu Kamo