Question

Have you ever wondered why a grocery store might pick a certain location to open? They will often pick a prime location because it is equidistant from three large housing developments. This is most likely the right place to open to make the most profit! There are three centers of intersection that occur within a triangle: the circumcenter, incenter, and centroid. Read below about the real-life applications of the incenter and centroid.

Pittsburgh, Pennsylvania is in the shape of a triangle formed by the meeting of two rivers the Allegheny and Monongahela which meet to form the Ohio River. It is a piece of land where the city was formed and became known as the Golden Triangle. A new computer store would like to open in the center of the city. Since the city was formed by a triangle and the computer store would like to maximize profit, they want their new location to be equidistant from each of the three sides of the triangle formed by the city. The incenter of the triangle formed by the city is where the computer store will open up its new location. Why? The incenter is the point in the triangle that has the same distance to each side of the triangle.

You are building a new desk for your room and decide to make it triangular in shape. You want to be able to put chairs on all three sides of the triangle so you want the legs to be in the center of the triangle. This is going to be tricky because you need to find the point where the triangle will balance in the center. This point where the triangle will balance is called the centroid. It is the point where all three medians of the sides of the triangle intersect.

Answer 1

The incenter of a triangle is the center of the circle that is inscribed inside the triangle and touches all three sides of the triangle. It is the point in the triangle that is equidistant from all three sides. The incenter is useful in situations where it is important to be equidistant from the sides of a triangle, such as in the example of a store wanting to be in the center of a city that is shaped like a triangle.

Explanation:

The centroid of a triangle is the point where the three medians of the triangle intersect. The medians of a triangle are lines that connect each vertex of the triangle to the midpoint of the opposite side. The centroid is also known as the center of mass or balance point of the triangle. It is useful in situations where it is important to find the center of balance of a triangle, such as in the example of building a triangular desk and wanting to place the legs in the center of the triangle.