Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{4a}\) \((211)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&2.125750467584&{}:{}&-0.395310994322&{}:{}&-0.730439473262&,\\B^\prime&{}\approx{}&6.729173723164&{}:{}&6.704718023924&{}:{}&-12.433891747089&,\\C^\prime&{}\approx{}&0.911655337330&{}:{}&-0.911655337330&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.730439473262\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-12.433891747089\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.684519413727\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.961910428851&{}:{}&-0.046834520438&{}:{}&-0.915075908413&. \end{alignedat} \]
4a (211)

Hiroyasu Kamo