What is the conclusion of the mathematical triangle?

The center of a triangle is the intersection of three internal bisectors; The center of the circumscribed circle of a triangle is called the outer center of the triangle; The outer center of a triangle is the intersection of the vertical lines of three sides.

The nature of the external world:

1. The perpendicular bisector of three sides of a triangle intersect at a point, which is the outer center of the triangle.

2. If O is the outer center of △ABC, ∠BOC=2∠A(∠A is acute angle or right angle) or ∠ BOC = 360-2 ∠ A (∠ A is obtuse angle).

3. When the triangle is an acute triangle, the outer center is inside the triangle; When the triangle is an obtuse triangle, the outer center is outside the triangle; When the triangle is a right triangle, the outer center is on the hypotenuse and coincides with the midpoint of the hypotenuse.

4. The distances from the outer center to the three vertices are equal.

Internal theorem

1, the three bisectors of the triangle intersect at one point. This point is the center of the triangle.

2. The distance from the center to the right-angled triangle is equal to half of the difference between the sum of two right-angled sides and the hypotenuse.

3.p is any point in the space where Δ ABC is located, and point 0 is the interior of Δ ABC if and only if vector P0=(a× vector PA+b× vector PB+c× vector PC)/(a+b+c).

4.o is the heart of the triangle, and A, B and C are the three vertices of the triangle. If the edge of the AO intersection BC extends to n, there is AO:ON=AB:BN=AC:CN=(AB+AC):BC.