Centroid of Triangle Calculator

A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The three medians of a triangle are concurrent at the centroid, which is also known as the center of gravity or center of mass of the triangle.

The centroid divides each median into two segments, with the ratio of the lengths of the two segments being 2:1. In other words, the distance from the centroid to the midpoint of a side is twice the distance from the centroid to the opposite vertex.

The centroid has important properties:-

1. It always lies inside the triangle.
2. It is equidistant from the three sides of the triangle.
3. It divides the triangle into six smaller triangles, each with the same area.
4. If the triangle is made of a homogeneous material, then the centroid is the balancing point of the triangle, and the triangle will balance on a point located at the centroid.
5. The centroid divides each median into two segments, one that is twice as long as the other.
6. The distance from the centroid to each vertex of the triangle is two-thirds of the length of the median that passes through that vertex.
7. The centroid of an equilateral triangle coincides with its circumcenter, incenter, and orthocenter.
8. The centroid of a right triangle is located on the hypotenuse, one-third of the distance from the right angle to the opposite vertex.
9. The centroid of an isosceles triangle lies on the line of symmetry.
10. The centroid of a triangle is the intersection point of the three medians, where each median is a line segment joining a vertex to the midpoint of the opposite side.