Derousseau's Generalization of the Malfatti circles

\[ \begin{alignedat}{4} I_{\mathbf{c}}&{}\approx{}&1.366025403784&{}:{}&2.366025403784&{}:{}&-2.732050807569&, \\ P_{\mathbf{1c}}&{}\approx{}&-0.124978685815&{}:{}&-0.475669247743&{}:{}&1.600647933559&, \\ P^-_{\mathbf{1c}}&{}\approx{}&0.155324995258&{}:{}&0.058559649996&{}:{}&0.786115354746&, \\ P^+_{\mathbf{1c}}&{}\approx{}&-0.574178390070&{}:{}&-1.331795938442&{}:{}&2.905974328512&, \\ Q_{\mathbf{1c}}&{}\approx{}&2.098379994211&{}:{}&2.788850523710&{}:{}&-3.887230517921&, \\ I^\prime_{\mathbf{1c}}&{}\approx{}&-0.669534957192&{}:{}&-1.719048506222&{}:{}&3.388583463414&, \end{alignedat} \]

\[ \begin{alignedat}{4} A^\prime_{\mathbf{1c}}&{}\approx{}&0.692992796309&{}:{}&-1.984525761239&{}:{}&2.291532964930&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-0.814313139868&{}:{}&0.185686860132&{}:{}&1.628626279737&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-3.039058011260&{}:{}&-5.263802882652&{}:{}&9.302860893912&, \\ A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.284457050376&{}:{}&-0.965925826289&{}:{}&3.250382876665&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.328808412459&{}:{}&-2.882361696309&{}:{}&4.211170108768&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.188104379956&{}:{}&-0.715925826289&{}:{}&1.904030206245&, \\ A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.436847386571&{}:{}&0.099613791793&{}:{}&1.337233594778&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.312754422633&{}:{}&-0.895635873797&{}:{}&1.582881451164&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.213504891485&{}:{}&0.080494267500&{}:{}&0.706000841015&, \\ A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-2.539058011260&{}:{}&3.539058011260&,\\B^*_{\mathbf{1c}}&{}\approx{}&-1.173032607476&{}:{}&0.000000000000&{}:{}&2.173032607476&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.429359733804&{}:{}&0.570640266196&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{2} \overrightarrow{{A}{A^\prime_{\mathbf{1c}}}}&{}\approx{}&-0.838759278774&\overrightarrow{{A}{I_{\mathbf{c}}}},\\\overrightarrow{{B}{B^\prime_{\mathbf{1c}}}}&{}\approx{}&-0.596118591655&\overrightarrow{{B}{I_{\mathbf{c}}}},\\\overrightarrow{{C}{C^\prime_{\mathbf{1c}}}}&{}\approx{}&-2.224744871392&\overrightarrow{{C}{I_{\mathbf{c}}}}. \end{alignedat} \] \[ \begin{alignedat}{4} I_{\mathbf{c}}&{}\approx{}&1.366025403784&{}:{}&2.366025403784&{}:{}&-2.732050807569&,\\ A^\prime_{\mathbf{1c}}&{}\approx{}&0.692992796309&{}:{}&-1.984525761239&{}:{}&2.291532964930&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-0.814313139868&{}:{}&0.185686860132&{}:{}&1.628626279737&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-3.039058011260&{}:{}&-5.263802882652&{}:{}&9.302860893912&. \end{alignedat} \]

\[ \begin{alignedat}{4} P_{\mathbf{1c}}&{}\approx{}&-0.124978685815&{}:{}&-0.475669247743&{}:{}&1.600647933559&,\\ A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.284457050376&{}:{}&-0.965925826289&{}:{}&3.250382876665&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.328808412459&{}:{}&-2.882361696309&{}:{}&4.211170108768&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.188104379956&{}:{}&-0.715925826289&{}:{}&1.904030206245&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^-_{\mathbf{1c}}&{}\approx{}&0.155324995258&{}:{}&0.058559649996&{}:{}&0.786115354746&,\\ A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.436847386571&{}:{}&0.099613791793&{}:{}&1.337233594778&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.312754422633&{}:{}&-0.895635873797&{}:{}&1.582881451164&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.213504891485&{}:{}&0.080494267500&{}:{}&0.706000841015&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^+_{\mathbf{1c}}&{}\approx{}&-0.574178390070&{}:{}&-1.331795938442&{}:{}&2.905974328512&,\\ A^\prime_{\mathbf{1c}}&{}\approx{}&0.692992796309&{}:{}&-1.984525761239&{}:{}&2.291532964930&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-0.814313139868&{}:{}&0.185686860132&{}:{}&1.628626279737&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-3.039058011260&{}:{}&-5.263802882652&{}:{}&9.302860893912&,\\ A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.284457050376&{}:{}&-0.965925826289&{}:{}&3.250382876665&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.328808412459&{}:{}&-2.882361696309&{}:{}&4.211170108768&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.188104379956&{}:{}&-0.715925826289&{}:{}&1.904030206245&, \end{alignedat} \]

\[ \begin{alignedat}{4} Q_{\mathbf{1c}}&{}\approx{}&2.098379994211&{}:{}&2.788850523710&{}:{}&-3.887230517921&,\\ A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-2.539058011260&{}:{}&3.539058011260&,\\B^*_{\mathbf{1c}}&{}\approx{}&-1.173032607476&{}:{}&0.000000000000&{}:{}&2.173032607476&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.429359733804&{}:{}&0.570640266196&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{4} I^\prime_{\mathbf{1c}}&{}\approx{}&-0.669534957192&{}:{}&-1.719048506222&{}:{}&3.388583463414&,\\ A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.284457050376&{}:{}&-0.965925826289&{}:{}&3.250382876665&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.328808412459&{}:{}&-2.882361696309&{}:{}&4.211170108768&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.188104379956&{}:{}&-0.715925826289&{}:{}&1.904030206245&,\\ A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-2.539058011260&{}:{}&3.539058011260&,\\B^*_{\mathbf{1c}}&{}\approx{}&-1.173032607476&{}:{}&0.000000000000&{}:{}&2.173032607476&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.429359733804&{}:{}&0.570640266196&{}:{}&0.000000000000&. \end{alignedat} \]