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The point equidistant from the three sides of a triangle is the center of the triangle. The center of the triangle is the point of intersection of the medians of the triangle. The medians of a triangle are the line segments that join the vertices of the triangle to the midpoints of the opposite sides.
It is the point known as the incentre.
The center of gravity of a triangle is its centroid. The centroid of a triangle is the intersection of the three medians.
centroid
centroid