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  • Perplex
    IB Math AIHL
    /
    Voronoi Diagrams
    /

    Problem Bank

    [Maximum mark: 5]

    Three existing water towers are located at the points

    ​
    A(0,0),B(8,0),C(0,6)
    ​

    where each grid unit represents ​1km. A new water tower is to be added to the diagram. To minimize risk of flooding, the water tower is placed at point ​P. A Voronoi diagram of the water towers is sketched below:

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    1. Determine:

      1. the coordinates of the point ​P​ that is equidistant from all ​3​ towers, and

        [3]

        To earn a crown, get your answer ready before you reveal the options!

      2. the common distance ​r​ from ​P​ to each tower.

        [2]

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