Apps. and Interpretation for IBDP Maths Ebook 1 | Page 139

4. The diagram below shows the Voronoi diagram of four apartments, A , B , C and D , in
�14 9 �
a city, where 1 unit represents 1 km. The points R and S � , � are the intersections of
� 3 2� the boundaries of Voronoi cells.
A new power station is going to be built in the city. It is suggested that the location of the
power station should be farthest from all apartments.
Two circles are constructed such that the centres are R and S respectively, and passes
through the apartments in adjacent Voronoi cells.
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(a) Find the radius of the circle centred at S .
[2]
The circle centred at S is the largest circle such that no apartment is located in the circle.
The radius of the circle centred at R is estimated as the greatest positive integer value
less than the radius of the circle centred at S .
(b) Write down the estimated value of the radius of the circle centred at R .
It is given that the actual value of the radius of the circle centred at R is
185
4
.
[1]
(c)
Find the percentage error in this estimate.
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[2]
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