Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{5a}\) \((213)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.122256164685&{}:{}&-0.058682959049&{}:{}&-0.063573205636&,\\B^\prime&{}\approx{}&1.278054161137&{}:{}&3.044886657820&{}:{}&-3.322940818957&,\\C^\prime&{}\approx{}&1.506052104307&{}:{}&-3.614525050336&{}:{}&3.108472946029&. \end{alignedat} \]
5a (213)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.097804931748\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-5.112216644549\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-6.024208417227\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
5a (213)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.253701868665&{}:{}&-0.037583132594&{}:{}&-0.216118736071&. \end{alignedat} \]
5a (213)

Hiroyasu Kamo