The formula for the circumscribed circle radius of an equilateral triangle

Method for finding the radius of the circumscribed circle of an equilateral triangle:

Let the side length of the regular triangle be a, then half the side length is a 2.

So the height of the triangle is [a -(a 2) ]= 3a 2.

Because it is a regular triangle, the four hearts are one

The height is 2:1, where the long is the circumscribed circle radius and the short is the inscribed circle radius.

So the radius of the circumscribed circle is r=2h 3=2*( 3a 2) 3= 3a 3.

An equilateral triangle (also known as a regular trilateral) is a triangle with three equal sides, and its three internal angles are equal, all of which are 60°, and it is a type of acute triangle. Equilateral triangles are also the most stable structure. Equilateral triangles are special isosceles triangles, so equilateral triangles have all the properties of isosceles triangles.

Ruler method:

You can draw a regular triangle by using a ruler to draw a regular triangle, and the method is quite simple: first draw a line segment of any length with a ruler (the length of this line segment determines the side length of the equilateral triangle), and then draw a circle with the two ends of the line segment as the center of the circle and the line segment as the radius, and the two circles converge at the two points, choose any point, and draw the line segment with the two ends of the original line segment, then the two line segments and the original line segment constitute a regular triangle.

Make a ray AC in the plane, take A as the fixed endpoint, intercept the line segment AB= equilateral triangle side length on the ray AC, and then keep the compass span with A and B as the end to make an arc at the same side point of AB, and the intersection point of the two arcs D is the third vertex of the triangle that is sought.

2 thirds of the root number 3. After the triangle.

The circles at each vertex are called the circumscribed circles of the triangle.

The methods for expressing the radius of the circumscribed circle of a triangle are:

1. Use the edges and corners of a triangle to represent the radius of its circumscribed circle.

2. Use the three sides of a triangle to represent the radius of its circumscribed circle.

3. The formula for expressing the radius of the circumscribed circle by the three sides and area of the triangle, etc.

Let the side length of the regular triangle be a, and the radius of the circumscribed circle is r=2h 3=2*( 3a 2) 3= 3a 3.

The circle that passes through the vertices of the triangle is called the circumscribed circle of the triangle, and the methods of expressing the radius of the circumscribed circle of the triangle are: using the sides and corners of the triangle to represent the radius of its circumscribed circle; Use the three sides of a triangle to represent the radius of its circumscribed circle; Formulas for expressing the radius of an inscribed circle with the three sides and area of a triangle, etc.

Circumscribed Circle Properties:1. The outer center of an acute triangle is inside the triangle.

2. The outer center of the right triangle is at the midpoint of the hypotenuse of the triangle.

3. The outer center of the obtuse triangle is outside the triangle.

4. The circle that passes through the three vertices of the triangle is called the circumscribed circle of the triangle, and its center is called the outer center of the triangle. In a triangle, the outer center of the triangle is not necessarily inside the triangle, but may be outside the triangle (e.g., an obtuse triangle) or on the side of the triangle (e.g., a right triangle).

Connecting the center of the circle and the vertices of the triangle, and making a perpendicular line on one side through the center of the circle, according to the Pythagorean theorem: it can be seen that if the side length of the regular triangle is a, then the radius of the circumscribed circle is three-thirds of the root number three a

You first draw the diagram, and the circumscribed circle radius, inscribed circle radius, and half the side length of the equilateral triangle form a right triangle, where the circumscribed circle radius is equal to twice the radius of the inscribed circle.

Let the radius of the circumscribed circle be r and the side length be a, then there is:

r=√3a/3

Equilateral trianglesThe outer cavity is connected to the circle radius formulais r= 3a 3.

The circumscribed circle radius formula of an equilateral triangle: the circumscribed circle radius, the inscribed circle radius, and half of the side length of the equilateral triangle form a right triangle.

where the radius of the circumscribed circle is equal to twice the radius of the tangent circle of the inner row. Let the radius of the circumscribed circle be r and the side length be a, then there is: r = 3a 3.

Finding the radius of an inscribed circle.

Set up a regular triangle.

If the length of the side is a, then the length of half the side is a 2. So the height of the triangle is [a -(a 2) ]= 3a 2.

Because it is a regular triangle, the four centers are one, and the height is 2:1, of which the long is the radius of the outer buried circle, and the short is the radius of the inscribed circle. So the radius of the circumscribed circle is r=2h 3=2*( 3a 2) 3= 3a 3.

The formula for the radius of the circumscribed circle of the triangle: abc 4r.

The area of the triangle is denoted as , the three sides are a, b, and c, and the radius of the circumscribed circle is r, then =abc 4r; r=abc 4 because =(1 2)ah=(1 2)absinc=(1 2)ab·c (2r)=abc 4r.

The circle passing through the vertices of the triangle is called the circumscribed circle of the triangle, and the methods of expressing the radius of the circumscribed circle of the triangle are:

1. Use the edges and corners of a triangle to represent the radius of its circumscribed circle.

2. Use the three sides of a triangle to represent the radius of its circumscribed circle.

3. The formula for expressing the radius of the circumscribed circle by the three sides and area of the triangle, etc.

Circumscribed Circle Properties:1. The outer center of an acute triangle is inside the triangle.

2. The outer center of the right triangle is at the midpoint of the hypotenuse of the triangle.

3. The outer center of the obtuse triangle is outside the triangle.

4. The circle that passes through the three vertices of the triangle is called the circumscribed circle of the triangle, and its center is called the outer center of the triangle, in the triangle, the outer center of the triangle is not necessarily inside the triangle, but may be outside the triangle (such as an obtuse triangle) or on the edge of the triangle (such as a right triangle).

Equilateral triangularThe formula for the radius of the circumscribed circle: Half of the circumscribed circle radius, inscribed circle radius, and side length of an equilateral triangleRight trianglewhere the radius of the circumscribed circle is equal to twice the radius of the inscribed circle.

Let the radius of the circumscribed circle be r and the side length be a, then there is: r = 3a 3. The formula of the radius of the circumscribed circle of the Yandong refers to the circle that passes through the vertices of the triangle is called the circumscribed circle of the triangle, and the methods of expressing the radius of the circumscribed circle of the triangle are: the sides and corners of the triangle are used to represent the radius of the circumscribed circle of the tanxiangque; Use the three sides of a triangle to represent the radius of its circumscribed circle; Formulas for expressing the radius of an inscribed circle with the three sides and area of a triangle, etc.

Properties: An equilateral triangle is an acute triangle, and the inner angles of the equilateral triangle are all equal, and both are 60°.

The middle line, the high line, and the bisector line on each side of the equilateral triangle overlap each other to allow the early conjunction (three lines in one).

An equilateral triangle is an axisymmetric figure that has three axes of symmetry, and the symmetry axis is the line on each side where the midline, high line, or diagonal bisector line is located.

4) Equilateral triangle center, inner and outer center.

The vertical center coincides at a point and is called the center of an equilateral triangle.

The sum of the distances from any point to three sides in an equilateral triangle is a fixed value (equal to its height).

An equilateral triangle has an isosceles triangle.

all nature.

TrianglesThe formula for the radius of the circumscribed circleAs follows:

The circle passing through the vertices of the triangle is called the circumscribed circle of the triangle, and the methods of expressing the radius of the circumscribed circle of the triangle are:

1. Use the edges and corners of a triangle to represent the radius of its circumscribed circle.

2. Use the three sides of a triangle to represent the radius of its circumscribed circle.

3. The formula for expressing the radius of the circumscribed circle by the three sides and area of the triangle, etc.

The nature of the circumscribed circle1. The outer center of an acute triangle.

Inside the triangle.

2. The outer center of the right-angled Changzi triangle is on the hypotenuse of the triangle.

Midpoint. Resistant to wheels.

3. Blunt angle. The outer center of the triangle is outside the triangle.

4. There is an outer center of the figure, there must be an external circle (the intersection of the perpendicular lines on each side, called Tong Jin to do the outer center).

TrianglesThe formula for the radius of the circumscribed circleYes: ABC 4R.

The area of the triangle is denoted as , the three sides are a, b, and c, and the radius of the circumscribed circle is r, then =abc 4r; r=abc 4 because =(1 2)ah=(1 2)absinc=(1 2)ab·c (2r)=abc 4r.

The circle passing through the vertices of the triangle is called the circumscribed circle of the triangle, and the methods of expressing the radius of the circumscribed circle of the triangle are:

1. Use the edges and corners of a triangle to represent the radius of its circumscribed circle.

2. Use the three sides of a triangle to represent the radius of its circumscribed circle.

3. The formula for expressing the radius of the circumscribed circle by the three sides and area of the triangle, etc.

Circumscribed Circle Properties:

1. Acute triangle outer center.

Inside the triangle.

2. Right triangles.

The outer center is obliquely accompanied by a triangle.

Midpoint. 3. Obtuse triangle.

The outer center is outside the triangle.

Fourth, the circle that passes through the three vertices of the trilukitan angle is called the circumscribed circle of the triangle, and its center is called the outer center of the triangle, in the triangle, the outer center of the triangle is not necessarily inside the triangle, it may be outside the triangle (such as an obtuse triangle) or on the edge of the triangle (such as a right-angled triangle).

Equilateral trianglesThe formula for the radius of the circumscribed circle

The circumscribed circle radius formula refers to the circumscribed circle of the triangle called the circumscribed circle of the triangle through the vertices of the triangle, and the methods of expressing the radius of the circumscribed circle of the triangle are: the sides and corners of the triangle are used to represent the radius of its circumscribed circle; Use the three sides of a triangle to represent the radius of its circumscribed circle; Formulas for expressing the radius of an inscribed circle with the three sides and area of a triangle, etc.

Properties: 1) An equilateral triangle is an acute triangle, the inner angles of the equilateral triangle are equal, and the macro and defeat years are all 60°.

2) The middle line, the high line, and the angular bisector on each side of the equilateral triangle coincide with each other. (Three lines in one.)

3) An equilateral triangle is an axisymmetric figure that has three axes of symmetry, and the axis of symmetry is the straight line where the middle line, the high line, or the bisector of the angle on each side are located.

4) Equilateral triangular center of gravity.

Inner and outer heart.

The vertical center coincides at the point where it is occluded, and is called the center of the equilateral triangle. (Four Hearts in One).

5) The sum of the distances from any point to three sides in an equilateral triangle is a fixed value. (equal to its height).