4 . The diagram below shows the Voronoi diagram of four convenience stores ,
A , B , C and D , in a city , where 1 unit represents 1 km . y
16
A ( 4, 14 )
B ( 12,14 )
C ( 12 , 8 )
The points E ( 8,11 ) and Voronoi cells .
�41 57 � F � , � � 7 7 � are the intersections of the boundaries of
Emily is going to start her business by opening a new convenience store at either E or F . She hopes that the location of the new convenience store to be as far as possible from all other convenience stores . Two circles are constructed such that the centres are E and F respectively , and passes through the convenience stores in adjacent Voronoi cells .
( a ) Find the radius of the circle centred at
( i ) E ;
( ii ) F . [ 4 ]
( b ) Hence , determine which location is farthest from all four convenience stores .
[ 1 ]
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