Apps. and Interpretation for IBDP Maths Ebook 1 | Page 137

2. The diagram below shows the Voronoi diagram of four landfills, A , B , C and D , in a
city, where 1 unit represents 1 km. The points E(5, 7.75) and F(5, 4.5) are the
intersections of the boundaries of Voronoi cells.
There are two hotels, one is located at E and the another one is located at F . Terence is
going to book a room in a hotel. He hopes that the location of the hotel selected to be as
far as possible from all other hair salons.
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Two circles are constructed such that the centres are E and F respectively, and passes
through the landfills in adjacent Voronoi cells.
(a) (i) Find the radius of the circle centred at E .
(ii) Find the radius of the circle centred at F .
(b)
(iii)
Hence, determine which hotel is farthest from all four landfills.
Find the difference of the circumferences of the two circles in (a).
[5]
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