An example: $C_1=[(0,0),1]\;,C_2=[(1,0),\frac{4}{5}]\;,C_3=[(2,\frac{3}{2}),\frac{3}{4}]\;.$

Contours show equal distance sums. $d_{\min}=\frac{3}{4}$ is achieved at $p_{\min} \approx (1.06, 0.80)$.

An example: $C_1=[(0,0),1]\;,C_2=[(1,0),\frac{4}{5}]\;,C_3=[(2,\frac{3}{2}),\frac{3}{4}]\;.$

Contours show equal distance sums. $d_{\min}=\frac{3}{4}$ is achieved at $p_{\min} \approx (1.06, 0.80)$.