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.

How would the position of the flag change if the field has n-sides and the teams have to start somewhere on the perimeter of the field?