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Three existing water towers are located at the points
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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Determine:
the coordinates of the point P that is equidistant from all 3 towers, and
the common distance r from P to each tower.
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A square park is modeled by the region 0≤x≤8 and 0≤y≤8 (all distances in meters).
There are three refreshment kiosks.
Kiosk A is at the point (2,6).
Kiosk B is at the point (2,b).
Kiosk C is at the point (6,6).
A Voronoi diagram of the park's kiosks is shown below:
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Every visitor is served by the nearest kiosk.
Show that V has coordinates (4,5).
Determine the value of b.
Determine the fraction of the park served by Kiosk A.
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