# Point of Concurrency

### Emaan Allawala - Geometry Project

## Scenario

Mrs. Johnson is installing a new triangular shaped counter in her kitchen. She wants to place the stove at the incenter of the triangle so that she has easy access to it from all sides of the counter.

## Pictorial Representation

## Coordinates of ΔABC:

A (0,12)

B (-12,0)

C (12,0)

## Triangle

## Construction of Incenter:

- Place the needle of the compass on point B of the triangle.
- Make an arc from that vertex that cuts through two sides of the triangle.
- Using those two points of intersection from the sides, make two more arcs that form an x.
- Once you have made the x, use a ruler and line it up with the vertex and draw a line.
- Repeat steps 1-4 for the other two points of the triangle.

**Incenter for ΔABC - (0,6)**

## Triangle With Incenter

## Calculations

## Explanation

The point of concurrency that best fits this scenario is the incenter because the incenter is equidistant from all of three triangle sides. The incenter represents where the stove will be placed on the counter. Mrs. Johnson wants the stove that is going to be placed on her triangular counter to be easily accessible from all three sides. This way the stove is right in the center if the counter, and she can easily get to it. In order to locate the incenter, angle bisectors and intersections within the triangle had to be found first.

Emaan Allawala

6th Period

12-17-14