A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle. The centroid is also called the center of gravity of the triangle.

The medians of a triangle are concurrent (they intersect in one common point). The point of concurrency of the medians is called the centroid of the triangle. The medians of a triangle are always concurrent in the interior of the triangle. The centroid divides the medians into a 2:1 ratio.

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The centroid of a triangle is the point where the three medians coincide. The centroid theorem states that the centroid is 23 of the distance from each vertex to the midpoint of the opposite side.

The first reason is two sides of the median triangle are equilateral. Equilateral means they are the same length. The second reason the base angles are congruent. Therefore, the median triangle cannot be a right triangle.

The definition of a median is the line segment from a vertex to the midpoint of the opposite side. It is also an angle bisector when the vertex is an angle in an equilateral triangle or the non-congruent angle of an isoceles triangle.

The Medians. In a triangle, a median is a line joining a vertex with the mid-point of the opposite side. Using the standard notations, in ΔABC, there are three medians: AMa, BMb, CMc. Three medians of a triangle meet at a point – centroid of the triangle.

The centroid of a triangle is the point at which the three medians meet. A median is the line between a vertex and the midpoint of the opposite side.

Steps to find the circumcenter of a triangle are:

1. Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC.
2. Calculate the slope of the particular line.
3. By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)
4. Find out the equation of the other line in a similar manner.

Simply construct the angle bisectors of the three angles of the triangle. The point where the angle bisectors intersect is the incenter. Actually, finding the intersection of only 2 angle bisectors will find the incenter.