Two delicate flowers were planted in a garden. the gardener, leslie, has a sprinkler that sprays water around in a circle. the closer a flower is to the sprinkler the more water it gets.
to be sure that her flowers each get the same amount of water, leslie needs to place the sprinkler where it will be the same distance from each of the flowers.
what are her choices about where to put the sprinkler? describe all the possibilities. (reminder the flowers are already in place, and leslie needs to adjust the position of the sprinkler relative to the flowers.)
Suppose leslie plants three flowers and wants to know if it will still be possible to place the sprinkler the same distance from all three.
determine which arrangements of the flowers (if any) will make this possible and which (if any) will make it impossible.
for those arrangements for which it will be possible, describe how leslie can find the correct location (or locations) for the sprinklers.
what about four flowers? five flowers? generalize as much as you can.