Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{2b}\) \((121)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.806562964876&{}:{}&1.947215248712&{}:{}&-2.753778213589&,\\B^\prime&{}\approx{}&-0.748302881333&{}:{}&2.806562964876&{}:{}&-1.058260083544&,\\C^\prime&{}\approx{}&-1.041196100146&{}:{}&1.041196100146&{}:{}&1.000000000000&. \end{alignedat} \]
2b (121)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-2.753778213589\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-1.058260083544\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.472473645917\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.707106781187&{}:{}&-0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
2b (121)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.242185659742&{}:{}&1.964060720257&{}:{}&-0.721875060515&. \end{alignedat} \]
2b (121)

Hiroyasu Kamo