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A city currently has four fire stations located at \(A(1,5)\), \(B(4,2)\), \(C(4,-2)\), and \(D(0,2)\).
The city council wants to build a **fifth fire station**. To maximize efficiency and coverage, the new station should be located at a point that is as far as possible from the existing stations (filling the largest gap in coverage).
The Voronoi diagram for the current stations has two internal vertices located at \(V_1(2, 3)\) and \(V_2(2, 0)\).
  1. Calculate the distance from vertex \(V_1\) to its nearest station \(A\).
  2. Calculate the distance from vertex \(V_2\) to its nearest station \(D\).
  3. Determine the coordinates of the optimal location for the new fire station \(E\). Justify your answer.

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