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]

\(\mathbf{5a}\) \((213)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.506618614285&{}:{}&-0.177900799442&{}:{}&-0.328717814843&,\\B^\prime&{}\approx{}&6.675870559770&{}:{}&6.659529783962&{}:{}&-12.335400343732&,\\C^\prime&{}\approx{}&1.364388631412&{}:{}&-1.364388631412&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.328717814843\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-12.335400343732\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-2.521061461906\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.541196100146&{}:{}&0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.932362994164&{}:{}&-0.031068625030&{}:{}&-0.901294369134&. \end{alignedat} \]
5a (213)

Hiroyasu Kamo