Capture the Flag Write-up

by

Martha Burns

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 n-sides and the teams have to start somewhere on the perimeter of the field?

Go to GSP Sketchpad and draw a scalene triangle with 3 line segments and label the vertices A, B, and C.

Highlight each line segment and construct its midpoint.

From each midpoint, construct a line perpendicular to each line segment.  Label the point D where the three lines intersect.

Hide the perpendicular lines and construct line segments from each vertex to point D.  Display the new segments as dashed lines with a different color.

Use the Sketchpad calculator and measure line segments AD, BD, and CD.

The three measures are equal, so this is the place the flag should be placed in order for the game to be fair.