Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{4a}\) \((211)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&2.806562964876&{}:{}&-0.748302881333&{}:{}&-1.058260083544&,\\B^\prime&{}\approx{}&1.947215248712&{}:{}&1.806562964876&{}:{}&-2.753778213589&,\\C^\prime&{}\approx{}&1.041196100146&{}:{}&-1.041196100146&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-1.058260083544\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-2.753778213589\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.472473645917\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.964060720257&{}:{}&-0.242185659742&{}:{}&-0.721875060515&. \end{alignedat} \]
4a (211)

Hiroyasu Kamo