A math problem

Answer: the three medians of a triangle intersect at a point which is twice as far from the vertex as it is from the midpoint of the opposite side. (Center of Gravity Theorem) This point of intersection is called the center of gravity of the triangle.

The perpendicular bisectors of the three sides of a triangle intersect at a point. (Outer Center Theorem) This point is called the outer center of the triangle.

The three heights of a triangle intersect at one point. (Perpendicular Center Theorem) This point is called the perpendicular center of the triangle.

The three interior angle bisectors of a triangle intersect at a point. (Interior Theorem) This point is called the interior of the triangle.

The bisector of one interior angle of a triangle intersects the exterior bisector at the other two vertices at one point. (Paracentric theorem) A triangle has three paracenters.

For the proof, refer to the following URL:

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