Derousseau's Generalization of the Malfatti circles

\[ \begin{alignedat}{4} I_{\mathbf{c}}&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&, \\ P_{\mathbf{5c}}&{}\approx{}&-0.128438083528&{}:{}&-0.038228759754&{}:{}&1.166666843281&, \\ P^-_{\mathbf{5c}}&{}\approx{}&-0.023239415330&{}:{}&0.093442780710&{}:{}&0.929796634620&, \\ P^+_{\mathbf{5c}}&{}\approx{}&-0.249245273290&{}:{}&-0.189436650952&{}:{}&1.438681924242&, \\ Q_{\mathbf{5c}}&{}\approx{}&-0.843511437593&{}:{}&0.375745287241&{}:{}&1.467766150353&, \\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.442293769655&{}:{}&-0.278630327865&{}:{}&1.720924097520&, \end{alignedat} \]

\[ \begin{alignedat}{4} A^\prime_{\mathbf{5c}}&{}\approx{}&-2.564755078384&{}:{}&-14.259020313537&{}:{}&17.823775391922&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.613130530351&{}:{}&0.591246313100&{}:{}&1.021884217251&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.137704095259&{}:{}&-0.183605460346&{}:{}&1.321309555605&, \\ A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.224897952433&{}:{}&-0.041496587389&{}:{}&1.266394539822&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.168558582526&{}:{}&-0.362542660834&{}:{}&1.531101243361&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.718955126836&{}:{}&-0.213992314916&{}:{}&1.932947441751&, \\ A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.104607008850&{}:{}&0.100873313667&{}:{}&1.003733695183&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.029895487332&{}:{}&-0.166207044387&{}:{}&1.196102531719&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.100297092599&{}:{}&0.403282057511&{}:{}&0.697015035088&, \\ A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.203820426377&{}:{}&0.796179573623&,\\B^*_{\mathbf{5c}}&{}\approx{}&-1.351229586822&{}:{}&0.000000000000&{}:{}&2.351229586822&,\\C^*_{\mathbf{5c}}&{}\approx{}&1.803275925284&{}:{}&-0.803275925284&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{2} \overrightarrow{{A}{A^\prime_{\mathbf{5c}}}}&{}\approx{}&-7.129510156769&\overrightarrow{{A}{I_{\mathbf{c}}}},\\\overrightarrow{{B}{B^\prime_{\mathbf{5c}}}}&{}\approx{}&-0.408753686900&\overrightarrow{{B}{I_{\mathbf{c}}}},\\\overrightarrow{{C}{C^\prime_{\mathbf{5c}}}}&{}\approx{}&-0.091802730173&\overrightarrow{{C}{I_{\mathbf{c}}}}. \end{alignedat} \] \[ \begin{alignedat}{4} I_{\mathbf{c}}&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&,\\ A^\prime_{\mathbf{5c}}&{}\approx{}&-2.564755078384&{}:{}&-14.259020313537&{}:{}&17.823775391922&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.613130530351&{}:{}&0.591246313100&{}:{}&1.021884217251&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.137704095259&{}:{}&-0.183605460346&{}:{}&1.321309555605&. \end{alignedat} \]

\[ \begin{alignedat}{4} P_{\mathbf{5c}}&{}\approx{}&-0.128438083528&{}:{}&-0.038228759754&{}:{}&1.166666843281&,\\ A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.224897952433&{}:{}&-0.041496587389&{}:{}&1.266394539822&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.168558582526&{}:{}&-0.362542660834&{}:{}&1.531101243361&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.718955126836&{}:{}&-0.213992314916&{}:{}&1.932947441751&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^-_{\mathbf{5c}}&{}\approx{}&-0.023239415330&{}:{}&0.093442780710&{}:{}&0.929796634620&,\\ A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.104607008850&{}:{}&0.100873313667&{}:{}&1.003733695183&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.029895487332&{}:{}&-0.166207044387&{}:{}&1.196102531719&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.100297092599&{}:{}&0.403282057511&{}:{}&0.697015035088&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^+_{\mathbf{5c}}&{}\approx{}&-0.249245273290&{}:{}&-0.189436650952&{}:{}&1.438681924242&,\\ A^\prime_{\mathbf{5c}}&{}\approx{}&-2.564755078384&{}:{}&-14.259020313537&{}:{}&17.823775391922&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-0.613130530351&{}:{}&0.591246313100&{}:{}&1.021884217251&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.137704095259&{}:{}&-0.183605460346&{}:{}&1.321309555605&,\\ A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.224897952433&{}:{}&-0.041496587389&{}:{}&1.266394539822&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.168558582526&{}:{}&-0.362542660834&{}:{}&1.531101243361&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.718955126836&{}:{}&-0.213992314916&{}:{}&1.932947441751&, \end{alignedat} \]

\[ \begin{alignedat}{4} Q_{\mathbf{5c}}&{}\approx{}&-0.843511437593&{}:{}&0.375745287241&{}:{}&1.467766150353&,\\ A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.203820426377&{}:{}&0.796179573623&,\\B^*_{\mathbf{5c}}&{}\approx{}&-1.351229586822&{}:{}&0.000000000000&{}:{}&2.351229586822&,\\C^*_{\mathbf{5c}}&{}\approx{}&1.803275925284&{}:{}&-0.803275925284&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{4} I^\prime_{\mathbf{5c}}&{}\approx{}&-0.442293769655&{}:{}&-0.278630327865&{}:{}&1.720924097520&,\\ A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.224897952433&{}:{}&-0.041496587389&{}:{}&1.266394539822&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.168558582526&{}:{}&-0.362542660834&{}:{}&1.531101243361&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.718955126836&{}:{}&-0.213992314916&{}:{}&1.932947441751&,\\ A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.203820426377&{}:{}&0.796179573623&,\\B^*_{\mathbf{5c}}&{}\approx{}&-1.351229586822&{}:{}&0.000000000000&{}:{}&2.351229586822&,\\C^*_{\mathbf{5c}}&{}\approx{}&1.803275925284&{}:{}&-0.803275925284&{}:{}&0.000000000000&. \end{alignedat} \]