Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{1a}\) \((013)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.044410501982&{}:{}&0.458682959049&{}:{}&0.496906538969&,\\B^\prime&{}\approx{}&-0.028054161137&{}:{}&0.955113342180&{}:{}&0.072940818957&,\\C^\prime&{}\approx{}&-0.672718770973&{}:{}&1.614525050336&{}:{}&0.058193720637&. \end{alignedat} \]
1a (013)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.764471598414\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.112216644549\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}2.690875083894\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
1a (013)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.078795346806&{}:{}&0.841108160721&{}:{}&0.237687186085&. \end{alignedat} \]
1a (013)

Hiroyasu Kamo