Question

Describe a triangle for which the centroid, circumcenter, incenter, and orthocenter are the same point. What features of this triangle cause these points to be concurrent? Complete the explanation

Answer 1

The type of triangle whose incenter, orthocenter, circumcenter and centroid are at the same point in the triangle is an Equilateral Triangle.

Explanation:

An equilateral triangle is a type of triangle which has all its three sides of equal length. Thus, all the three angles are of equal size of 60 degrees. As a result of the equal size in the three lengths, all lines drawn from the sides, angles, or inter-sectors will meet at the same point at the center of the triangle.

The incenter, located at the intersection of the angle bisectors, circumcenter, located at the intersection of the perpendicualr bisectors of the sides, the centroid, located at the intersection of the medians and the orthocenter, located at the intersections of the altitudes are all on the same point in the triangle.

Answer 2

An equilateral triangle

Explanation:

Because an equilateral has a feature that all sides have the same length and all angles are of the same, it does not matter from which side and peak the centroid, circumcenter, incenter and orthocenter is created, they would always end up at the same point.