Point of Concurrency Project

Problem

It's Sofie's birthday and her and her friends, Lilly and Anna, want to meet up to go to a movie theater. They need a meeting spot that's an equal distance from all their homes so they can walk to the movie theater together.

Steps

1. Place the compass at one vertex of the triangle and open it to a little more than half of the segment.
2. Draw an arc from the vertex.
3. Repeat this process from the other vertices of the triangle and draw the arcs long enough to cross with the other arcs.
4. Then draw a line through the two intersecting points of the arcs you created. This is the perpendicular line.
5. Repeat the previous step with the other sides of the triangle to create the circumcenter.

Explanation

The best point of concurrency to solve the scenario is circumcenter. The circumcenter represents where the three girls will meet to go to the movies at an equal distance from their homes so that they travel at the same distance. The special segment used was perpendicular bisector.