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The four hearts of a triangle and their important inferences?
1, center of gravity: the intersection of three midlines of a triangle. This point must be within a triangle.

And this point divides each midline into 2: 1.

2. Inner heart: the intersection of three bisectors of a triangle. This point must be within a triangle.

And the distance from the point to the three sides is equal, which is also the center of the inscribed circle of the triangle. ..

3. Exterior center: the intersection of three vertical lines of a triangle. The point of acute triangle is inside the triangle, and the point of obtuse triangle is outside the triangle.

The distance from this point to the three vertices of the triangle is equal, and it is also the center of the circumscribed circle of the triangle.

4. Vertical center: the intersection of three heights of a triangle. The point of acute triangle is inside the triangle, and the point of obtuse triangle is outside the triangle.