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The Voronoi diagram for four towns \(A, B, C\), and \(D\) has two internal vertices located at \(V_1(2, 3)\) and \(V_2(4, 1)\). The coordinates of the towns are \(A(0,2)\), \(B(3,1)\), \(C(4,2)\), and \(D(4,0)\).
We want to locate a toxic dump as far as possible from any town.
  1. Calculate the distance from vertex \(V_1\) to its nearest site \(A(0,2)\).
  2. Calculate the distance from vertex \(V_2\) to its nearest site \(D(4,0)\).
  3. Which of these two vertices is the best location for the toxic dump? What is the radius of the empty circle there?

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