Derousseau's Generalization of the Malfatti circles

\[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&, \\ P_{\mathbf{6}}&{}\approx{}&0.499910807065&{}:{}&0.499910807065&{}:{}&0.000178385870&, \\ P^-_{\mathbf{6}}&{}\approx{}&1.048341617171&{}:{}&1.048341617171&{}:{}&-1.096683234343&, \\ P^+_{\mathbf{6}}&{}\approx{}&0.401447312137&{}:{}&0.401447312137&{}:{}&0.197105375726&, \\ Q_{\mathbf{6}}&{}\approx{}&0.517012249752&{}:{}&0.517012249752&{}:{}&-0.034024499505&, \\ I^\prime_{\mathbf{6}}&{}\approx{}&0.493661940902&{}:{}&0.493661940902&{}:{}&0.012676118196&, \end{alignedat} \]

\[ \begin{alignedat}{4} A^\prime_{\mathbf{6}}&{}\approx{}&0.382683432365&{}:{}&0.216772751325&{}:{}&0.400543816310&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.216772751325&{}:{}&0.382683432365&{}:{}&0.400543816310&,\\C^\prime_{\mathbf{6}}&{}\approx{}&6.526234467956&{}:{}&6.526234467956&{}:{}&-12.052468935912&, \\ A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.419607974722&{}:{}&0.580184994736&{}:{}&0.000207030542&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.580184994736&{}:{}&0.419607974722&{}:{}&0.000207030542&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.299728091845&{}:{}&0.299728091845&{}:{}&0.400543816310&, \\ A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.088619529491&{}:{}&1.921812845662&{}:{}&-2.010432375154&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.921812845662&{}:{}&1.088619529491&{}:{}&-2.010432375154&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.328227057688&{}:{}&0.328227057688&{}:{}&0.343545884624&, \\ A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.070445884989&{}:{}&-0.070445884989&,\\B^*_{\mathbf{6}}&{}\approx{}&1.070445884989&{}:{}&0.000000000000&{}:{}&-0.070445884989&,\\C^*_{\mathbf{6}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{2} \overrightarrow{{A}{A^\prime_{\mathbf{6}}}}&{}\approx{}&0.834089318960&\overrightarrow{{A}{I}},\\\overrightarrow{{B}{B^\prime_{\mathbf{6}}}}&{}\approx{}&0.834089318960&\overrightarrow{{B}{I}},\\\overrightarrow{{C}{C^\prime_{\mathbf{6}}}}&{}\approx{}&25.111377834540&\overrightarrow{{C}{I}}. \end{alignedat} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&,\\ A^\prime_{\mathbf{6}}&{}\approx{}&0.382683432365&{}:{}&0.216772751325&{}:{}&0.400543816310&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.216772751325&{}:{}&0.382683432365&{}:{}&0.400543816310&,\\C^\prime_{\mathbf{6}}&{}\approx{}&6.526234467956&{}:{}&6.526234467956&{}:{}&-12.052468935912&. \end{alignedat} \]

\[ \begin{alignedat}{4} P_{\mathbf{6}}&{}\approx{}&0.499910807065&{}:{}&0.499910807065&{}:{}&0.000178385870&,\\ A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.419607974722&{}:{}&0.580184994736&{}:{}&0.000207030542&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.580184994736&{}:{}&0.419607974722&{}:{}&0.000207030542&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.299728091845&{}:{}&0.299728091845&{}:{}&0.400543816310&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^-_{\mathbf{6}}&{}\approx{}&1.048341617171&{}:{}&1.048341617171&{}:{}&-1.096683234343&,\\ A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.088619529491&{}:{}&1.921812845662&{}:{}&-2.010432375154&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&1.921812845662&{}:{}&1.088619529491&{}:{}&-2.010432375154&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.328227057688&{}:{}&0.328227057688&{}:{}&0.343545884624&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^+_{\mathbf{6}}&{}\approx{}&0.401447312137&{}:{}&0.401447312137&{}:{}&0.197105375726&,\\ A^\prime_{\mathbf{6}}&{}\approx{}&0.382683432365&{}:{}&0.216772751325&{}:{}&0.400543816310&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.216772751325&{}:{}&0.382683432365&{}:{}&0.400543816310&,\\C^\prime_{\mathbf{6}}&{}\approx{}&6.526234467956&{}:{}&6.526234467956&{}:{}&-12.052468935912&,\\ A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.419607974722&{}:{}&0.580184994736&{}:{}&0.000207030542&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.580184994736&{}:{}&0.419607974722&{}:{}&0.000207030542&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.299728091845&{}:{}&0.299728091845&{}:{}&0.400543816310&, \end{alignedat} \]

\[ \begin{alignedat}{4} Q_{\mathbf{6}}&{}\approx{}&0.517012249752&{}:{}&0.517012249752&{}:{}&-0.034024499505&,\\ A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.070445884989&{}:{}&-0.070445884989&,\\B^*_{\mathbf{6}}&{}\approx{}&1.070445884989&{}:{}&0.000000000000&{}:{}&-0.070445884989&,\\C^*_{\mathbf{6}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{4} I^\prime_{\mathbf{6}}&{}\approx{}&0.493661940902&{}:{}&0.493661940902&{}:{}&0.012676118196&,\\ A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.419607974722&{}:{}&0.580184994736&{}:{}&0.000207030542&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.580184994736&{}:{}&0.419607974722&{}:{}&0.000207030542&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.299728091845&{}:{}&0.299728091845&{}:{}&0.400543816310&,\\ A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.070445884989&{}:{}&-0.070445884989&,\\B^*_{\mathbf{6}}&{}\approx{}&1.070445884989&{}:{}&0.000000000000&{}:{}&-0.070445884989&,\\C^*_{\mathbf{6}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]