Capture the Flag
Three teams, A, B, and C, each start from a vertex of a scalene triangular field. Their goal is to be the first team to grab the flag that is located inside the triangular field. If the game is fair, then each team has to run the same distance to get to the flag.
Where should the flag be positioned for the game to be fair? Describe how you found the position.

Extensions 
How would the position of the flag change if the field has nsides and the teams have to start somewhere on the perimeter of the field?

Related External Resources 
Triangle Centers with Sketchpad [ GSP sketch ]
Explore the altitudes, angle bisectors, medians, and perpendicular bisectors of a triangle and make conjectures about the behavior of those very special segments.
Submit your idea for an investigation to InterMath.
