Triangles Incentre, Circumcentre, Orthocentre, Centroid Significances

Incentre

The significance of the incentre is a point where the radius must be drawn from to have the biggest possible circle which touches all of the sides of the triangle.

The incentre always remains inside the triangle as the name suggests because the circle it is the centre of must be located inside the triangle

After we tested the four different triangles (2 by computer 2 by hand) the significance of the incentre we stated at the beginning was correct; the incentre is a point which always remains within the triangle and is the point where the radius must be drawn from to have the biggest possible circle which touches all of the sides of the triangle.

Centroid

The significance of the centroid is that it is the point of geometric centre for a polygon otherwise known as the centre of mass for the triangle which makes the centroid the equivalent of centre of gravity in three dimensional shapes.

The centroid always remains inside of the triangle because it is the exact centre for the triangle.

By using the four different triangles (2 on computer 2 by hand) we found that all the points using the rules of finding the centroid proved our beginning statement is correct; that the centroid is indeed the geometric centre of the triangle and all the centroids for each triangle remained inside the triangle.

Orthocentre

The significance of the orthocentre is that it is the point of intersection for all three altitudes of a triangle.

One fact we have uncovered by having a look at our four different triangles is that the orthocenter will only be located outside the triangle if one of the triangles angles is over 90 degrees.

After we tested the four different triangles (2 by computer 2 by hand) the