Apps. and Interpretation for IBDP Maths Ebook 1 | Page 136

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 36
1. The diagram below shows the Voronoi diagram of four hair salons, A , B , C and D , in
a city, where 1 unit represents 1 km. The points E(4.125, 5) and F(5, 5) are the
intersections of the boundaries of Voronoi cells.
Raina is going to start her business by opening a new hair salon at either E or F . She
hopes that the location of the new hair salon to be as far as possible from all other hair
salons.
Two circles are constructed such that the centres are E and F respectively, and passes
through the hair salons in adjacent Voronoi cells.
(a) (i) Find the exact radius of the circle centred at E .
(ii) Write down the radius of the circle centred at F .
(b)
(iii)
Hence, determine which location is farthest from all four hair salons.
Write down the total distance from F to all other four hair salons.
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