Solve {l}{(3-w)^{2}+(-1-r)^{2}=r^{2}}{(1-4)^{2}+(3-w)^{2}=r^{2}}{(-6-u)+(2-r)^2=r^2}{(-5-w)+(-5-v)^2=r^2}

$$\left.\begin{array} { l } { ( 3 - w ) ^ { 2 } + ( - 1 - r ) ^ { 2 } = r ^ { 2 } } \\ { ( 1 - 4 ) ^ { 2 } + ( 3 - w ) ^ { 2 } = r ^ { 2 } } \\ { ( - 6 - u ) + ( 2 - r ) ^ { 2 } = r ^ { 2 } } \\ { ( - 5 - w ) + ( - 5 - v ) ^ { 2 } = r ^ { 2 } } \end{array} \right\}$$

Solve for w, r, u, v

$$r=-4\text{, }w=\sqrt{7}+3\approx 5.645751311\text{, }u=14\text{, }v=-\left(\sqrt{\sqrt{7}+24}+5\right)\approx -10.161952277$$

$$r=-4\text{, }w=\sqrt{7}+3\approx 5.645751311\text{, }u=14\text{, }v=\sqrt{\sqrt{7}+24}-5\approx 0.161952277$$

$$r=-4\text{, }w=3-\sqrt{7}\approx 0.354248689\text{, }u=14\text{, }v=-\left(\sqrt{24-\sqrt{7}}+5\right)\approx -9.621065753$$

$$r=-4\text{, }w=3-\sqrt{7}\approx 0.354248689\text{, }u=14\text{, }v=\sqrt{24-\sqrt{7}}-5\approx -0.378934247$$