Shark Attack

By: Allison K. Kootsikas

Guppy, Tadpole, and Goldfish beach surround Equilateral Sea. Why do you think
Equilateral Sea is named that way?

Tiger shark and his family swim together in the Equilateral Sea. When the
family gets hungry, Tiger makes sure they stay in one place (so he doesn't lose
them), and then finds food at each of the beaches. Tiger gets food at one beach
at a time because he can only hold so much food in his mouth at one time. So he
gets food at one beach, comes back to share the food (red square), and then
repeats the process at the other beaches.

Where should Tiger place his family in the Equilateral Sea in order to swim the
**least** distance for his three hunting trips? Explain your reasoning.

The first step in this is to construct an equilateral triangle using GSP. To do this, construct a circle and its radius. Then construct a circle from the radius and point. Connect the intersection and center points and an equilateral triangle is formed.

The next step is to hide the circles, leaving an
equilateral triangle. All three sides
are the same distance.

The first thing I tried to do was to just put
points on the triangle and move them until the distance was small. Here are the steps I went through to find
that method.

The next step is to construct a point on each side
of the triangle. Also construct a point inside of the triangle and make segments
from the inner point to the sides.

The next step is to measure the lengths of the
segments and add them up. By moving the
center point around, you will find the shortest distance.

After investigating what would occur if I entered
random points, I decided to find out what happened if I found the intersection
of the angle bisectors (incenter) and the intersection of the midpoints
(centroid).

Click here to see my GSP
sketch.

I found that it did not matter if the centroid,
the incenter, or random points were used to determine the shortest distance the
shark would have to travel to bring food to his babies.