Three towns X, Y and Z are such that Y is 20 km from X and 22 km from Z. Town X is
18 km from Z. A Health Centre is to be built by the government to serve the three
towns. The Centre is to be located such that patients from X and Y will always travel
equal distances to access the Health Centre while patients from Z will travel exactly
10 km to reach the health Centre.
(a) Using a Scale of 1cm to 2km, find by Construction, using a pair of compasses and ruler only, the possible positions the Health Centre can be located.
(b) In how many possible locations can the health Centre be built?
(c) Measure and record the distances of the locations from town X.
(d) Which of these locations would be convenient for all the three towns?
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