What is the side center of a triangle and where is the side center of a triangle?

Centricity: The intersection of the outer bisector of any two corners of the triangle and the inner bisector of the third corner.

A triangle has three paracentricities, and it must be outside the triangle, and the triangle formed by the three paracentrics of the triangle is called a paracentric triangle.

1. The center of the circumscribed circle is called the side center of the triangle.

2. A circle tangent to one side of the triangle and the extension lines on both sides is called a tangent circle of the triangle.

The nature of the paracentric triangle.

Let the circumscribed circle i1(r1) of abc in a tangent line and the extension line of ab tangent to point p1. The radius of the inscribed circle is r.

1. One of the inner bisectors of a triangle intersects with the outer bisector of the other two angles, and the point is the side center of the triangle. 2. The distance from the side center to the three sides of the triangle is equal.

3. The triangle has three side cut circles and three side centers. The center must be outside the triangle.

4、∠bi1c=90°-∠a/2.

5、ap1=r1·cot(a/2)=(a+b+c)/2.

6、∠ai1b=∠c/2.

7、s⊿abc=r1(b+c-a)/2.

8、r1=rp(p-a).

9、r1=(p-b)(p-c)/r.

r1+1/r2+1/r3=1/r.

11、r1=r/(tanb/2)(tanc/2).

12. The radius of the circumscribed circle on the hypotenuse of a right triangle is equal to half of the circumference of the triangle.

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The center of the circle next to the triangle is referred to as the triangle side center ruler answer.

It is the intersection of the bisector of one inner angle of the triangle and the bisector of the outer angle of the other two inner angles; Obviously, any triangle has three side-cut circles and three side-centers.

Property 1: The bisector of one of the inner corners of a triangle intersects with the outer bisectors of the other two corners, which is the center of the triangle.

Property 2: The distance from the side center to the three sides of the triangle is equal.

Property 3: The triangle has three circumscribed circles and three paracentricities. The center must be outside the triangle.

Property 4: The radius of the circumscribed circle on the hypotenuse of a right triangle is equal to half the circumference of the triangle.

The triangle centroid theorem --- triangle intersects one of the inner bisectors and the outer bisectors at the other two vertices at a point.

1. If a triangle intersects at a point where the bisector of an inner angle and the bisector of the outer angle at the other two vertices intersect at one point, the point is the center of the triangle.

2. Each triangle has three side centers.

3. The distance from the side center to the three sides is equal. Point M is a mess of ABC. The intersection of the outer bisector of any two corners of the triangle and the inner bisector of the third corner. A triangle has three paracentricities, and it must be outside the triangle.

4. The center of the triangle: only the regular triangle has a center, and then the center of gravity, the inner heart, the outer heart, the vertical center, and the four hearts are one.

The center of the circumscribed circle of the triangle, referred to as the paracenter of the triangle, is the intersection of the bisector of one inner angle of the triangle and the bisector of the outer angle of the other two inner angles; Obviously, any triangle has three side-cut circles and three thick side-centers.

Properties: Property 1] Perpendicular center of an acute triangle.

within the triangle; Right-angled triangle.

is centered at a right-angled vertex; The perpendicular center of an obtuse triangle is outside the triangle.

Nature 2] The vertical center of the triangle is the heart of the triangle that perpetuates its feet; In other words, the heart of the triangle is the vertical center of the triangle next to it.

Property 3] Perpendicular o The points of symmetry on the three sides are all in the circumscribed circle of abc.

on the circle. Property 4] In ABC, there are six groups of four-point circles.

There are three groups (each group of four states) similar right-angled triangles.

Property 5] O, A, B, and C are the perpendicular centers of triangles with the other three vertices (and such four points are called perpendicular groups).

Property 6] The circumscribed circle of ABC, ABO, BCO, ACO is equicircular.

Property 7] The distance from any vertex of the triangle to the vertical center is equal to 2 times the distance from the outer center to the opposite side.

Triangle Features:

1. The inner part of the triangle is the center of the inscribed circle of the triangle, that is, the intersection of the three corners of the triangle and the flat ground division, and the distance from it to the three sides of the triangle is equal.

2. The triangular object trace is outside the center of the town.

It is the center of the circumscribed circle of the triangle, that is, the perpendicular bisector of the three sides of the triangle.

, which is at an equal distance from the three vertices of the triangle.

3. Triangular center of gravity.

is the intersection of the midlines of the triangle's three sides, and its distance from the vertex is twice its distance from the midpoint of the opposite side.

The center of the triangle is referred to as the center of the triangle, which is the intersection of the bisector of one inner angle of the triangle and the bisector of the other two inner angles. Obviously, any finger triangle has three side high circles and three side centers.

Here's how to do it

One of the inner bisectors of the triangle and the outer angles of the other two corners intersect the simple dividice at a point where the triangle is the center of the triangle.

The nature of the sidelines.

1. The bisector of the inner angle of the triangle and the bisector of the outer angle at the other two vertices intersect at one point, which is the side center of the triangle.

2. Each triangle has three side centers.

Curve 3, the distance from the center to the three sides is equal.