# Point of Concurrency: The Giver

### By Avery Davis

## Problem:

The Giver, an older man who keeps the memories and emotions of the town so that they are not lost forever, has given all of these memories to Jonas, the new receiver, who has been chosen to learn to hold them and keep them from the general public. Unfortunately, the Giver had also given away some of the memories he needed to find his way to the central plaza for the night's ceremony. The Giver wanders around lost, unsure of what to do, until he remembers that the central plaza lies at a point of concurrency between three of the only buildings he can remember. The plaza lays at the circumcenter of the auditorium, the law and justice building, and the town hall. The Giver must find this location before he misses the ceremony and gets in trouble.

## Best Point of Concurrency

The best Point of Concurrency for this project is the circumcenter. This is because the circumcenter is an equal distance away from each vertex, making it more applicable to the problem since the central plaza is an equal distance from the three locations.

## Construction:

## Scale: 1 in= 10 ft

## Steps:

1. Place the tip of a compass onto one of the vertices of the triangle. Open the other end so that the compass stretches wider than half the segment being bisected.

2. Create an arc.

3. Place the tip of the compass onto the vertex at the other end of the segment, leaving the measurement setting of the compass the same.

4. Create a second arc.

5. These arcs should intersect in two places. Take a ruler and draw a line through the two places where the arcs intersect each other.

6. This gives you the perpendicular bisector. Repeat all steps for each segment of the triangle. You will end up with three perpendicular bisectors.

7. The Point of Concurrency, the circumcenter, is where all of the perpendicular bisectors meet. Place a point here.

## Calculations:

## Explanation:

The best Point of Concurrency for my problem is the circumcenter because I am trying to find a point that is an equal distance from each vertex, or location. The circumcenter found represents the central plaza, the location which the Giver must get to for the ceremony. Now that the circumcenter/central plaza has been found, he can arrive in time and not get in trouble. The special segments used to locate my point were the perpendicular bisectors of the triangle. The perpendicular bisectors intersect at the circumcenter, which is how the central plaza was found. The circumcenter was accurate in the problem, because the correct location of the central plaza was discovered.