Derousseau's Generalization of the Malfatti circles

\(A=22.5\degree\), \(B=22.5\degree\), \(C=135\degree\).

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

\(\mathbf{5c}\) \((312)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-56.920974110168&{}:{}&-68.322447379109&{}:{}&126.243421489277&,\\B^\prime&{}\approx{}&-0.984042025213&{}:{}&0.165769452762&{}:{}&1.818272572451&,\\C^\prime&{}\approx{}&-0.523335716201&{}:{}&-0.523335716201&{}:{}&2.046671432402&. \end{alignedat} \]
5c (312)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-10.401473268942\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.149811477976\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.079673118742\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&6.568535592272&{}:{}&6.568535592272&{}:{}&-12.137071184544&. \end{alignedat} \]
5c (312)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-1.359155018361&{}:{}&-0.915409495002&{}:{}&3.274564513363&. \end{alignedat} \]
5c (312)

Hiroyasu Kamo