Derousseau's Generalization of the Malfatti circles

\[ \begin{alignedat}{4} I_{\mathbf{a}}&{}\approx{}&-1.000000000000&{}:{}&1.000000000000&{}:{}&1.000000000000&, \\ P_{\mathbf{6a}}&{}\approx{}&1.086689796779&{}:{}&-0.078020817101&{}:{}&-0.008668979678&, \\ P^-_{\mathbf{6a}}&{}\approx{}&0.902075806737&{}:{}&0.017354031954&{}:{}&0.080570161309&, \\ P^+_{\mathbf{6a}}&{}\approx{}&1.310992966503&{}:{}&-0.193899797618&{}:{}&-0.117093168886&, \\ Q_{\mathbf{6a}}&{}\approx{}&1.448018475480&{}:{}&-0.672027713219&{}:{}&0.224009237740&, \\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.555852595253&{}:{}&-0.416889446440&{}:{}&-0.138963148813&, \end{alignedat} \]

\[ \begin{alignedat}{4} A^\prime_{\mathbf{6a}}&{}\approx{}&1.244016935856&{}:{}&-0.122008467928&{}:{}&-0.122008467928&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&5.098076211353&{}:{}&1.000000000000&{}:{}&-5.098076211353&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&1.098076211353&{}:{}&-1.098076211353&{}:{}&1.000000000000&, \\ A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.806952388982&{}:{}&-0.726257150084&{}:{}&-0.080695238898&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.229422863406&{}:{}&-0.219615242271&{}:{}&-0.009807621135&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.334097441518&{}:{}&-0.095783886799&{}:{}&-0.238313554719&, \\ A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.474645386743&{}:{}&0.093102842536&{}:{}&0.432251770720&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.008837226334&{}:{}&-0.098942933031&{}:{}&0.090105706697&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.085585763082&{}:{}&0.020884375660&{}:{}&-0.106470138742&, \\ A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.500000000000&{}:{}&-0.500000000000&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.866025403784&{}:{}&0.000000000000&{}:{}&0.133974596216&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{2} \overrightarrow{{A}{A^\prime_{\mathbf{6a}}}}&{}\approx{}&-0.122008467928&\overrightarrow{{A}{I_{\mathbf{a}}}},\\\overrightarrow{{B}{B^\prime_{\mathbf{6a}}}}&{}\approx{}&-5.098076211353&\overrightarrow{{B}{I_{\mathbf{a}}}},\\\overrightarrow{{C}{C^\prime_{\mathbf{6a}}}}&{}\approx{}&-1.098076211353&\overrightarrow{{C}{I_{\mathbf{a}}}}. \end{alignedat} \] \[ \begin{alignedat}{4} I_{\mathbf{a}}&{}\approx{}&-1.000000000000&{}:{}&1.000000000000&{}:{}&1.000000000000&,\\ A^\prime_{\mathbf{6a}}&{}\approx{}&1.244016935856&{}:{}&-0.122008467928&{}:{}&-0.122008467928&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&5.098076211353&{}:{}&1.000000000000&{}:{}&-5.098076211353&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&1.098076211353&{}:{}&-1.098076211353&{}:{}&1.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{4} P_{\mathbf{6a}}&{}\approx{}&1.086689796779&{}:{}&-0.078020817101&{}:{}&-0.008668979678&,\\ A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.806952388982&{}:{}&-0.726257150084&{}:{}&-0.080695238898&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.229422863406&{}:{}&-0.219615242271&{}:{}&-0.009807621135&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.334097441518&{}:{}&-0.095783886799&{}:{}&-0.238313554719&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^-_{\mathbf{6a}}&{}\approx{}&0.902075806737&{}:{}&0.017354031954&{}:{}&0.080570161309&,\\ A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.474645386743&{}:{}&0.093102842536&{}:{}&0.432251770720&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.008837226334&{}:{}&-0.098942933031&{}:{}&0.090105706697&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.085585763082&{}:{}&0.020884375660&{}:{}&-0.106470138742&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^+_{\mathbf{6a}}&{}\approx{}&1.310992966503&{}:{}&-0.193899797618&{}:{}&-0.117093168886&,\\ A^\prime_{\mathbf{6a}}&{}\approx{}&1.244016935856&{}:{}&-0.122008467928&{}:{}&-0.122008467928&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&5.098076211353&{}:{}&1.000000000000&{}:{}&-5.098076211353&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&1.098076211353&{}:{}&-1.098076211353&{}:{}&1.000000000000&,\\ A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.806952388982&{}:{}&-0.726257150084&{}:{}&-0.080695238898&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.229422863406&{}:{}&-0.219615242271&{}:{}&-0.009807621135&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.334097441518&{}:{}&-0.095783886799&{}:{}&-0.238313554719&, \end{alignedat} \]

\[ \begin{alignedat}{4} Q_{\mathbf{6a}}&{}\approx{}&1.448018475480&{}:{}&-0.672027713219&{}:{}&0.224009237740&,\\ A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.500000000000&{}:{}&-0.500000000000&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.866025403784&{}:{}&0.000000000000&{}:{}&0.133974596216&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{4} I^\prime_{\mathbf{6a}}&{}\approx{}&1.555852595253&{}:{}&-0.416889446440&{}:{}&-0.138963148813&,\\ A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.806952388982&{}:{}&-0.726257150084&{}:{}&-0.080695238898&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.229422863406&{}:{}&-0.219615242271&{}:{}&-0.009807621135&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.334097441518&{}:{}&-0.095783886799&{}:{}&-0.238313554719&,\\ A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.500000000000&{}:{}&-0.500000000000&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.866025403784&{}:{}&0.000000000000&{}:{}&0.133974596216&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&. \end{alignedat} \]