Difference between radius and diameter. How to find the circumference of a circle: through diameter and radius

A circle is a curved line that is formed from all points equidistant from one specific point, which is called the center of the circle. In another way, we can give the following definition of a circle: a curve that is closed on a plane, and all points of which, lying in the same plane as the curve, are removed from the center at the same distance. Each point on the circle is the same distance from the center of the circle.

Definition

Radius is a straight line segment that connects every point on a circle that is equidistant from the center of the circle to the center of the circle.

Diameter is a straight line segment that connects any two points on a circle that are distant from each other and must always pass through the center of this circle.

Comparison

The radius is the line segment that connects each point on the circle that is equidistant from the center of the circle to the center of the circle. The radius is denoted by the letter R. It shows the length of this segment. The center of the circle is indicated by the letter O.

The diameter is a straight line segment that must always pass through the center of the circle and connect any two points of the circle that are distant from each other. Any such straight segment is called a diameter and is denoted by the letter D. The length of the diameter is also denoted by the letter D.

Let points A, B be on the circle itself, then segments OA, OB are the radii of this circle.

Their lengths are equal: OB=OA.

BA = OB + OA, since BA = D, and OA = OB = R, then D = 2R.

The diameter will be equal to two radii. D = 2R. Accordingly, the radius will be equal to half the diameter: R = D/2.

Conclusions website

1. The diameter is always equal to twice the radius of the circle.
2. The radius of a circle is equal to half the diameter of that circle. R = D/2

What is the definition? What are the center, radius, chord and diameter of a circle?

1. Class
2. Diameter is a segment connecting two points on a circle and passing through the center of the circle,
3. Circle is the geometric locus of points in the plane equidistant from a given point, called the center, at a given non-zero distance, called the radius
   The radius is not only a distance value, but also a segment connecting the center of the circle with one of its points
   A segment connecting two points on a circle is called a chord. The chord passing through the center of the circle is called the diameter
   Diameter is a chord (a segment connecting two points) on a circle (sphere, surface of a ball), and passing through the center of this circle (sphere, ball). The length of this segment is also called diameter. The diameter of a circle is the chord passing through its center; such a chord has a maximum length. The diameter is equal in size to two radii.
4. the definition is recognized by the presence in the phrase of the word CALLED, which is an explanation of a certain concept. the properties of which are beginning to be studied 9 the majority Passes by.... past)
   called a circle
   geometric figure. consisting of points of the plane. located at the same distance from one point. called the center of the environment.
   radius - segment. connecting the center of a circle to any point on the circle.
   chord - segment. connecting 2 points on a circle
   diameter - chord. passing through the center of the circle. the length of the diameter is equal to the length of 2 radii.

   TEXTBOOK stolen evil people?
   access to the search was blocked by older comrades?

5. The center is a point from which all points in the vicinity are at the same distance.
   radius - a segment from the center to any point in the surrounding area.
   Diameter is a segment connecting two points on a circle and passing through the center.
   A chord is a segment connecting two points on a circle. Doesn't have to go through the center. Good luck! ! It's simple))
6. Homework (02/09/2016)
   This homework must be completed in A4 format.
   Read paragraph 22 Circle. Circumference.
   Write down the definition of the circle, center, radius and diameter of a circle (using the Internet or any math reference book).
   Draw Figure 87(b) page 146, from page 147 write down two formulas for finding the circumference of a circle through the radius and diameter of the circle. Write down the value of the number.
   Complete tests 2, 3, 4 on page 153 of the textbook.
   Read paragraph 23 Circle. Area of ​​a circle.
   Write down the definition of a circle (p. 153).
   Draw a circle, mark the center, radius and diameter of the circle.
   Write down two formulas to find the area of ​​a circle using the radius and diameter of the circle:
   ;
   675 (c, d), 676 (c, d), 678 (c, d. There is no need to draw a circle, you need to find the diameter and radius).
   Read paragraph 23 Ball. Sphere.
   Fill out the table

   Objects shaped like a sphere
   (name and drawing of the object) Objects shaped like a ball (name and drawing of the object)
   1
   2
   3

   Draw a picture 103 page 158, write down the formulas for the volume of a sphere and the area of ​​a sphere (page 158)
   690, 691, 692. try to solve

7. eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

This lesson is devoted to the study of circumference and circle. The teacher will also teach you to distinguish between closed and open lines. You will become familiar with the basic properties of a circle: center, radius and diameter. Learn their definitions. Learn to determine the radius if the diameter is known, and vice versa.

If you fill the space inside the circle, for example, draw a circle using a compass on paper or cardboard and cut it out, you will get a circle (Fig. 10).

Rice. 10. Circle

Circle- this is the part of the plane limited by a circle.

Condition: Vitya Verkhoglyadkin drew 11 diameters in his circle (Fig. 11). And when he recalculated the radii, he got 21. Did he count correctly?

Rice. 11. Illustration for the problem

Solution: There should be twice as many radii as diameters, therefore:

Vitya counted incorrectly.

Bibliography

1. Mathematics. 3rd grade. Textbook for general education institutions with adj. per electron carrier. At 2 hours Part 1 / [M.I. Moreau, M.A. Bantova, G.V. Beltyukova and others] - 2nd ed. - M.: Education, 2012. - 112 p.: ill. - (School of Russia).
2. Rudnitskaya V.N., Yudacheva T.V. Mathematics, 3rd grade. - M.: VENTANA-COUNT.
3. Peterson L.G. Mathematics, 3rd grade. - M.: Yuventa.

1. Mypresentation.ru ().
2. Sernam.ru ().
3. School-assistant.ru ().

Homework

1. Mathematics. 3rd grade. Textbook for general education institutions with adj. per electron carrier. At 2 hours Part 1 / [M.I. Moreau, M.A. Bantova, G.V. Beltyukova and others] - 2nd ed. - M.: Education, 2012., Art. 94 No. 1, Art. 95 No. 3.

2. Solve the riddle.

My brother and I live together,

We have so much fun together

We will place a mug on the sheet (Fig. 12),

Let's trace it with a pencil.

We got what we needed -

It's called...

3. It is necessary to determine the diameter of the circle if it is known that the radius is 5 m.

4. * Using a compass, draw two circles with radii: a) 2 cm and 5 cm; b) 10 mm and 15 mm.

Circumference called a closed, plane curve, all points of which, lying in the same plane, are located at the same distance from the center.

Dot ABOUT is the center of the circle, R is the radius of the circle - the distance from any point on the circle to the center. By definition, all radii of a closed

rice. 1

the curves have the same length.

The distance between two points on a circle is called a chord. A segment of a circle passing through its center and connecting two of its points is called a diameter. The midpoint of the diameter is the center of the circle. Points on a circle divide a closed curve into two parts, each part is called a circular arc. If the ends of the arc belong to the diameter, then such a circle is called a semicircle, the length of which is usually denoted π . The degree measure of two circles that have common ends is 360 degrees.

Concentric circles are circles that have a common center. Orthogonal circles are circles that intersect at an angle of 90 degrees.

The plane enclosed by a circle is called a circle. One part of the circle, which is limited by two radii and an arc, is a circular sector. A sector arc is an arc that bounds a sector.

Rice. 2

The relative position of a circle and a straight line (Fig. 2).

A circle and a straight line have two points in common if the distance from the straight line to the center of the circle is less than the radius of the circle. In this case, the straight line in relation to the circle is called a secant.

A circle and a straight line have one common point if the distance from the straight line to the center of the circle is equal to the radius of the circle. In this case, the line in relation to the circle is called tangent to the circle. Their common point is called the tangency point of the circle and the line.

Basic circle formulas:

• C = 2πR , Where C - circumference
• R = С/(2π) = D/2 , Where С/(2π) — length of the arc of a circle
• D = C/π = 2R , Where D - diameter
• S = πR2 , Where S - area of ​​a circle
• S = ((πR2)/360)α , Where S — area of ​​the circular sector

The circle and the circle got their name in Ancient Greece. Already in ancient times, people were interested in round bodies, so the circle became the crown of perfection. The fact that a round body could move on its own was the impetus for the invention of the wheel. It would seem, what is special about this invention? But imagine if in an instant the wheels disappear from our lives. This invention later gave rise to the mathematical concept of a circle.

And how is it different from a circle? Take a pen or colors and draw a regular circle on a piece of paper. Paint over the entire middle of the resulting figure with a blue pencil. The red outline indicating the boundaries of the shape is a circle. But the blue content inside it is the circle.

The dimensions of a circle and a circle are determined by the diameter. On the red line indicating the circle, mark two points so that they are mirror images of each other. Connect them with a line. The segment will definitely pass through the point in the center of the circle. This segment connecting opposite parts of a circle is called a diameter in geometry.

A segment that does not extend through the center of the circle, but joins it at opposite ends, is called a chord. Consequently, the chord passing through the center point of the circle is its diameter.

Diameter is denoted by the Latin letter D. You can find the diameter of a circle using values ​​such as area, length and radius of the circle.

The distance from the central point to the point plotted on the circle is called the radius and is denoted by the letter R. Knowing the value of the radius helps to calculate the diameter of the circle in one simple step:

For example, the radius is 7 cm. We multiply 7 cm by 2 and get a value equal to 14 cm. Answer: D of the given figure is 14 cm.

Sometimes you have to determine the diameter of a circle only by its length. Here it is necessary to apply a special formula to help determine Formula L = 2 Pi * R, where 2 is a constant value (constant), and Pi = 3.14. And since it is known that R = D * 2, the formula can be presented in another way

This expression is also applicable as a formula for the diameter of a circle. Substituting the quantities known in the problem, we solve the equation with one unknown. Let's say the length is 7 m. Therefore:

Answer: the diameter is 21.98 meters.

If the area is known, then the diameter of the circle can also be determined. The formula that applies in this case looks like this:

D = 2 * (S / Pi) * (1 / 2)

S - in this case Let's say in the problem it is equal to 30 square meters. m. We get:

D = 2 * (30 / 3, 14) * (1 / 2) D = 9, 55414

When the value indicated in the problem is equal to the volume (V) of the ball, the following formula for finding the diameter is used: D = (6 V / Pi) * 1 / 3.

Sometimes you have to find the diameter of a circle inscribed in a triangle. To do this, use the formula to find the radius of the represented circle:

R = S/p (S is the area of ​​the given triangle, and p is the perimeter divided by 2).

We double the result obtained, taking into account that D = 2 * R.

Often you have to find the diameter of a circle in everyday life. For example, when determining what is equivalent to its diameter. To do this, you need to wrap the finger of the potential owner of the ring with thread. Mark the points of contact of the two ends. Measure the length from point to point with a ruler. We multiply the resulting value by 3.14, following the formula for determining the diameter with a known length. So, the statement that knowledge of geometry and algebra is not useful in life is not always true. And this is a serious reason for taking school subjects more responsibly.