Suppose three teams, A,
B, and C , are to play a game of capture the flag. Each team begins
in a different position. The starting points for the team can
be connected to form a triangle.
The goal of the game is
to capture a flag, and return it to your team's starting point.
Assuming the triangle is scalene, where should the flag be placed
to ensure a fair game?
Begin by constructing the
perpendicular bisectors for all three sides the triangle. The
point where these three lines intersect is called the circumcenter,
and is equal distance from all three vertices.
By making a script in GSP,
I can try this with any three starting positions for the teams. Click here to open the script. Open
a new sketch under File in GSP. Choose any three points. Click
on the script itself, and then click on play. The computer should
find the circumcenter of the triangle for you.
I chose this assignment
in part, because of my own memories of playing "Capture the
Flag." I think students would really enjoy this assignment,
because it ties in with their own background knowledge as well.
This shows a very real application of geometry concepts.