Derousseau's Generalization of the Malfatti circles

\[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&, \\ P_{\mathbf{7}}&{}\approx{}&0.499552854332&{}:{}&0.499552854332&{}:{}&0.000894291336&, \\ P^-_{\mathbf{7}}&{}\approx{}&-0.170483256580&{}:{}&-0.170483256580&{}:{}&1.340966513159&, \\ P^+_{\mathbf{7}}&{}\approx{}&0.353623965370&{}:{}&0.353623965370&{}:{}&0.292752069260&, \\ Q_{\mathbf{7}}&{}\approx{}&0.465678818685&{}:{}&0.465678818685&{}:{}&0.068642362630&, \\ I^\prime_{\mathbf{7}}&{}\approx{}&0.486023490490&{}:{}&0.486023490490&{}:{}&0.027953019020&, \end{alignedat} \]

\[ \begin{alignedat}{4} A^\prime_{\mathbf{7}}&{}\approx{}&0.076120467489&{}:{}&0.324423348821&{}:{}&0.599456183690&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.324423348821&{}:{}&0.076120467489&{}:{}&0.599456183690&,\\C^\prime_{\mathbf{7}}&{}\approx{}&6.474538827970&{}:{}&6.474538827970&{}:{}&-11.949077655939&, \\ A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.617885940244&{}:{}&0.381431227821&{}:{}&0.000682831935&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.381431227821&{}:{}&0.617885940244&{}:{}&0.000682831935&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.200271908155&{}:{}&0.200271908155&{}:{}&0.599456183690&, \\ A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-1.636887027219&{}:{}&-0.384067935279&{}:{}&3.020954962498&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.384067935279&{}:{}&-1.636887027219&{}:{}&3.020954962498&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.101264812114&{}:{}&0.101264812114&{}:{}&0.797470375771&, \\ A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.871533517609&{}:{}&0.128466482391&,\\B^*_{\mathbf{7}}&{}\approx{}&0.871533517609&{}:{}&0.000000000000&{}:{}&0.128466482391&,\\C^*_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{2} \overrightarrow{{A}{A^\prime_{\mathbf{7}}}}&{}\approx{}&1.248302881333&\overrightarrow{{A}{I}},\\\overrightarrow{{B}{B^\prime_{\mathbf{7}}}}&{}\approx{}&1.248302881333&\overrightarrow{{B}{I}},\\\overrightarrow{{C}{C^\prime_{\mathbf{7}}}}&{}\approx{}&24.912465467161&\overrightarrow{{C}{I}}. \end{alignedat} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&,\\ A^\prime_{\mathbf{7}}&{}\approx{}&0.076120467489&{}:{}&0.324423348821&{}:{}&0.599456183690&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.324423348821&{}:{}&0.076120467489&{}:{}&0.599456183690&,\\C^\prime_{\mathbf{7}}&{}\approx{}&6.474538827970&{}:{}&6.474538827970&{}:{}&-11.949077655939&. \end{alignedat} \]

\[ \begin{alignedat}{4} P_{\mathbf{7}}&{}\approx{}&0.499552854332&{}:{}&0.499552854332&{}:{}&0.000894291336&,\\ A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.617885940244&{}:{}&0.381431227821&{}:{}&0.000682831935&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.381431227821&{}:{}&0.617885940244&{}:{}&0.000682831935&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.200271908155&{}:{}&0.200271908155&{}:{}&0.599456183690&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^-_{\mathbf{7}}&{}\approx{}&-0.170483256580&{}:{}&-0.170483256580&{}:{}&1.340966513159&,\\ A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-1.636887027219&{}:{}&-0.384067935279&{}:{}&3.020954962498&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.384067935279&{}:{}&-1.636887027219&{}:{}&3.020954962498&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.101264812114&{}:{}&0.101264812114&{}:{}&0.797470375771&. \end{alignedat} \]

\[ \begin{alignedat}{4} P^+_{\mathbf{7}}&{}\approx{}&0.353623965370&{}:{}&0.353623965370&{}:{}&0.292752069260&,\\ A^\prime_{\mathbf{7}}&{}\approx{}&0.076120467489&{}:{}&0.324423348821&{}:{}&0.599456183690&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.324423348821&{}:{}&0.076120467489&{}:{}&0.599456183690&,\\C^\prime_{\mathbf{7}}&{}\approx{}&6.474538827970&{}:{}&6.474538827970&{}:{}&-11.949077655939&,\\ A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.617885940244&{}:{}&0.381431227821&{}:{}&0.000682831935&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.381431227821&{}:{}&0.617885940244&{}:{}&0.000682831935&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.200271908155&{}:{}&0.200271908155&{}:{}&0.599456183690&, \end{alignedat} \]

\[ \begin{alignedat}{4} Q_{\mathbf{7}}&{}\approx{}&0.465678818685&{}:{}&0.465678818685&{}:{}&0.068642362630&,\\ A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.871533517609&{}:{}&0.128466482391&,\\B^*_{\mathbf{7}}&{}\approx{}&0.871533517609&{}:{}&0.000000000000&{}:{}&0.128466482391&,\\C^*_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]

\[ \begin{alignedat}{4} I^\prime_{\mathbf{7}}&{}\approx{}&0.486023490490&{}:{}&0.486023490490&{}:{}&0.027953019020&,\\ A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.617885940244&{}:{}&0.381431227821&{}:{}&0.000682831935&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.381431227821&{}:{}&0.617885940244&{}:{}&0.000682831935&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.200271908155&{}:{}&0.200271908155&{}:{}&0.599456183690&,\\ A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.871533517609&{}:{}&0.128466482391&,\\B^*_{\mathbf{7}}&{}\approx{}&0.871533517609&{}:{}&0.000000000000&{}:{}&0.128466482391&,\\C^*_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]