It is the centroid.
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There are absolutely 0 parallel lines in any given triangle.
Yes. Any triangle can be inscribed within a circle, although the center of the circle may not necessarily lie within the triangle.
The incentre, which is the point at which the angle bisectors meet.
The center of gravity of a triangle is its centroid. The centroid of a triangle is the intersection of the three medians.
Center of mass of an equilateral triangle is located at its geometric center (centroid).