Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{7}\) \((222)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.448502526124&{}:{}&0.264718787460&{}:{}&0.286778686416&,\\B^\prime&{}\approx{}&0.733914302124&{}:{}&-1.642091487647&{}:{}&1.908177185523&,\\C^\prime&{}\approx{}&1.165631799079&{}:{}&2.797516317790&{}:{}&-2.963148116870&. \end{alignedat} \]
7 (222)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.661796968651\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}4.403485812745\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}6.993790794476\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
7 (222)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.689709175272&{}:{}&0.191395671947&{}:{}&0.118895152781&. \end{alignedat} \]
7 (222)

Hiroyasu Kamo