How to divide a circle into 4 equal parts

Type 1: Make two perpendicular diameters through the center of the circle.

Type 2: Take point A on the circle as the starting point, the radius of the circle is the length, use the compass to find the two upper six equal points, b, c, b between a and c.

Connect BC, make the perpendicular bisector of BC, and intersect the circle at point D, at this time the arc AD is 1 4 circumference, measure the length of AD for the compass, and take the point on the circle in turn to quartet the circumference. Connect the quartile points.

The first two are quartile shapes, the essence of which is to find diameters perpendicular to each other.

The third type: the area is divided into 4 parts.

With the center of the circle as the center of the circle, and the radius of the circle as the radius of 1 2 as the radius to make concentric circles, the area of the small circle is 1 4 of the large circle, and then the outer circle can be divided into 3 equal parts. 3. Needless to say, the divisions are equal.

Fourth: it is still a quartile of the area.

Make the diameter of the great circle ab, take oa and ob as the diameter to make two circles, the area of these two circles is 1 4 of the great circle, and divide the remaining part of the great circle into two halves.

1.Take any two points A and B on the arc. Connect the two points.

2.The perpendicular bisector of the straight line AB intersects at two points C and D, connecting CD.

3.Make a perpendicular bisector of a straight line cd, intersecting circles and two points of e and f.

d, e, f are the quarters of the circle. The intersection of CD and EF is the center of the circle.

Cross-cut method. I've calculated that there should be three ways to cut it.

You try.

1. Draw a circle with a compass;

2. Do not change the distance between the two feet of the compass, and find a point A on the circle to be the center of the circle, and the arc of the year is intersected in B and C;

3. Also do not change the distance between the two feet of the compass, and draw an arc with the point b as the center of the circle to cross the circle at a and d;

4. Also do not change the distance between the two feet of the compass, and draw an arc with the point d as the center of the circle to cross the circle in b and e;

Then arc bc = arc ce = arc eb

The circumferential angle is 360°.

Divided into 6 equal parts, that is, each corner is 360 6 = 60°.

If there are 30°, 60°, 90° triangles, you can divide them directly.

Or fold the circle in half first, and then fold it in half along the radius, connecting the crease with the intersection point of the circle and the center of the circle, and the angle between this line and the radius is 60°.

Hello 1, first fold the circle in half.

2. Fold in half along the radius.

3. Connect the intersection of the crease and the circle with the center of the circle, and the angle between the line and the radius is 60°4, and it is smoothly divided into 6 parts.

This is very easy to solve, 6 equal parts, one is 60 degrees, then the center of the circle and the six points link should be 6 equilateral triangles, you use the compass to draw an arbitrary circle of any radius, the radius remains still, draw a point on the circumference, and then use the compass to take this point as the starting point and then intercept 5 segments, you will get 6 equal parts of 6 points!

360 6 = 60 degrees, and each central angle is 60 degrees.

Six 60-degree fan-shaped pieces of the same size form a circle.

1. Draw a circle with a compass;

2. Do not change the distance between the feet of the compass, and find a point on the circle first.

Version A is the center of the circle to draw an arc and cross circles.

Authority to b, c;

3. Also do not change the distance between the two feet of the compass, and draw an arc with the point b as the center of the circle to cross the circle at a and d;

4. Also do not change the distance between the two feet of the compass, and draw an arc with the point d as the center of the circle to cross the circle in b and e;

Then arc bc = arc ce = arc eb

1. Divide into 6 equal parts first. (Compass arcs on a circle with radius).

2. Divide the sixth-equal arc equally, and then divide it equally. (Bisector arc, that is, to make the chord length perpendicular bisector).

The parts are separated, and 2 parts are counted as one point, not three points. It's easy to do with just a compass and a ruler.

Draw a radius, rotate 120 degrees clockwise around the center of the circle to get another radius, and then rotate 120 degrees in the same direction to get another radius, and these three radii will divide the circle into three parts.

Draw each corner 120 degrees at the midpoint.

Each sector is 120 degrees, divided.

A circle is a geometric figure that refers to the set of all points in a plane at a fixed distance to a fixed point. This given point is called the center of the circle. The distance that is a fixed value is called the radius of the circle.

When a line segment rotates in a plane around one of its endpoints, the trajectory of its other endpoint is a circle. The diameter of the circle is innumerable; There are countless lines on the axis of symmetry of the circle. The diameter of the circle is 2 times the radius, and the radius of the circle is half the diameter.

When drawing a circle with a compass, the point where the tip of the needle is located is called the center of the circle, which is generally represented by the letter O. The line segment connecting the center of the circle to any point on the circle is called the radius, which is generally represented by the letter r, and the length of the radius is the distance between the two corners of the compass. The line segment that passes through the center of the circle and ends on both ends of the circle is called the diameter, which is generally represented by the letter D.

A circle is a curved figure on a plane, an axisymmetric figure, its axis of symmetry is the straight line where the diameter is located, and the circle has an infinite number of axes of symmetry.

There are 4 ways to divide a circle into 4 equal parts.

How to divide a circle into quarters equally:

The first is to make two diameters perpendicular to each other through the center of the circle. (The shape and area of each division are the same).

The second way: take any point on the circle A as the dot, the radius of the circle as the radius as the circle, and intersect the original circle at the two points b and c. Connect BC, make the perpendicular bisector of BC intersect at point D, and then make the perpendicular bisector of AD intersect at E and F, then A, D, E, F are the quartile points of the circle (AD and EF are perpendicular, same as Method 1).

(The shape and area of each division are the same).

The third type: take the center of the circle as the center of the circle, and take the radius of the circle (1 2), (2 points of the root number 2), (2 points of the root number 3) as the radius, and make three concentric circles, then these 3 concentric circles divide the original circle into 4 parts of equal area. (Each division has a different shape and the same area).

Fourth: through the center of the circle o as the diameter ab, with the midpoint of oa and ob as the center of the circle, with oa and ob as the diameter, make two circles, the area of these two circles is 1 4 of the great circle. The remaining part of the great circle is then divided into two halves along the ab flat to achieve a quarter circle.

The shape of each aliquot is the same and the area is the same).

1. Two vertical diameters, a whole circle, divided into four 90° sectors.

2. Divide a diameter into 3 points and 5 equal parts, take the rightmost point as the center of the circle, and take the radius of the great circle 1 2 as the radius of the small circle to make a small circle, and in the same way, take the leftmost point as the center of the circle, and make a small circle with the radius of the great circle 1 2. The 2 small circles are exactly cut to the center of the circle. The area of each minor circle is 1 4

The remaining part of the great circle is 1 2 of the total area, which is bisected by two irregular figures.

3. Sit on 4 concentric circles, with a radius ratio of 1: root number 2: root number 3: 2The outermost circle thus obtained is divided into 4 equal parts.

Type 1: Make two perpendicular diameters through the center of the circle.

Type 2: Start from point A on the circle, and use the radius of the circle as the length, using a compass.

Find the two upper sixths of the equinox, b, c, and b between a and c.

Connect BC and make a perpendicular bisector of BC.

Intersect with the circle at point d, at this time the arc ad is 1 4 circumference, measure the length of ad for the compass, and take the point on the circle in turn to quartet the circumference. Connect the quartile points.

The first two are quartile shapes, the essence of which is to find diameters perpendicular to each other.

The third type: the area is divided into 4 parts.

Take the center of the circle as the center of the circle, and take the radius of the circle 1 2 as the radius to make concentric circles.

Then the area of the small circle is 1 4 of the large circle, and then the outer circle can be divided into 3 equal parts. 3. Needless to say, the divisions are equal.

Fourth: it is still a quartile of the area.

To make the diameter of the great circle ab, take OA and ob as the diameter to make two circles, the area of these two circles.

They are all 1 4 of the Great Circle, and the rest of the Great Circle is divided into two halves.