Derousseau's Generalization of the Malfatti circles

\(a:b:c=5:12:13\).

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

\(\mathbf{7a}\) \((233)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.018702774091&{}:{}&-0.008977331564&{}:{}&-0.009725442528&,\\B^\prime&{}\approx{}&1.433384247027&{}:{}&3.293414795243&{}:{}&-3.726799042270&,\\C^\prime&{}\approx{}&0.902498713713&{}:{}&-2.165996912912&{}:{}&2.263498199199&. \end{alignedat} \]
7a (233)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.014962219273\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-5.733536988108\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-3.609994854854\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
7a (233)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.063325529863&{}:{}&-0.031876082646&{}:{}&-0.031449447216&. \end{alignedat} \]
7a (233)

Hiroyasu Kamo