Solve for x_c (complex solution)
x_{c}=\sqrt{-y_{c}^{2}+30y_{c}-150}+6
x_{c}=-\sqrt{-y_{c}^{2}+30y_{c}-150}+6
Solve for y_c (complex solution)
y_{c}=\sqrt{39+12x_{c}-x_{c}^{2}}+15
y_{c}=-\sqrt{39+12x_{c}-x_{c}^{2}}+15
Solve for x_c
x_{c}=\sqrt{-y_{c}^{2}+30y_{c}-150}+6
x_{c}=-\sqrt{-y_{c}^{2}+30y_{c}-150}+6\text{, }y_{c}\geq 15-5\sqrt{3}\text{ and }y_{c}\leq 5\sqrt{3}+15
Solve for y_c
y_{c}=\sqrt{39+12x_{c}-x_{c}^{2}}+15
y_{c}=-\sqrt{39+12x_{c}-x_{c}^{2}}+15\text{, }x_{c}\geq 6-5\sqrt{3}\text{ and }x_{c}\leq 5\sqrt{3}+6
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