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 travel equal distance to access the health centre while patients from Z will travel exactly 10 km to reach the Health centre.

(a) Using a scale of 1 cm to 2 km, find the 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 location from town X.

(d) Which of these locations would be convenient for all three towns?