Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{6a}\) \((231)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.069165380380&{}:{}&-0.033199382582&{}:{}&-0.035965997798&,\\B^\prime&{}\approx{}&2.259078156460&{}:{}&4.614525050336&{}:{}&-5.873603206796&,\\C^\prime&{}\approx{}&0.852036107425&{}:{}&-2.044886657820&{}:{}&2.192850550395&. \end{alignedat} \]
6a (231)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.055332304304\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-9.036312625840\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-3.408144429699\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
6a (231)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.155053746175&{}:{}&-0.120891299397&{}:{}&-0.034162446779&. \end{alignedat} \]
6a (231)

Hiroyasu Kamo