The knowledge of the genie arc online. Kolo that of inscriptions kut. Visual guide (2019)

Colo, yogo parts, їх development and communication - speeches, with which jewelry is permanently stuck. Kiltsya, bracelets, casts, pipes, coolers, spirals - a lot of all round robots. How is it that all the time is porahuvati, especially how you spared the school to skip the lessons of geometry?

Let's take a look at how it smelt parts and how it stinks.

• Kolo - lіnіya, scho I will surround the colo.
• The arc is a part of the stake.
• Radius - vidrizok, which is the center of the stake, as a point of the stake.
• Horda - from the point of the stake.
• The segment is a part of the stake, surrounded by a chord and an arc.
• The sector is a part of the stake, surrounded by two radii and an arc.

The magnitude that will cite us is the same value:

Now, as a matter of fact, as a zavdannya, tied with pieces of stake, it is brought to virishuvati.

• To know the end of the rosigorta, be it a part of the ring (bracelet). Assignments diameter and chord (option: diameter and central cut), know the arc's length.
• Є little ones on the area, you need to know about their size in the projection of the letter in an arc. Set the arc and the diameter, know the jordi.
• Diznat the visota of details, otrimanoy zginannyam flat workpieces in an arc. Variants of vykhidnykh danikh: additional arc and diameter, additional arc and chord; Visually the height of the segment.

Life, even if only for the first time, but I don't have to, in order to show the need for a set of two parameters for the knowledge of all of them. The axis of the tsim mi will be occupied. And itself, there are five parameters of the segment: D, L, X, φ and H. Potentially, you can bet on them, you can bet on them, and by the way of the brain storm all the people know.

It’s not trivial for the reader, I will not guide the lecturer’s decisions, but I’ll guide the results in the formulas (ie, there is no formal solution, I’ll discuss it along the way).

One more respect: about one vimira. All sizes, except for the central kut, are immersed in the quiet, abstract ones themselves. It means that if, for example, you set one value in millimeters, then I don’t need to set it in centimeters, but the resulting value is in quiet millimeters (and the area is in square millimeters). The same can be said about inches, feet and sea miles.

I only the central kut depends on the degree and not the least. That is why, as practice shows, people who design more round, are not shy in the radio. The phrase “kut pi na chotiri” should be put at the deaf kut, tody yak “kut forty five degrees” - zoosulya everything, oskil tse all five degrees is more for the norm. However, all formulas will have an intermediate value of more than one cut - α. Behind the zmіstom, half of the central kuta, vimіryana in radіans, even in the whole sense, you can spokіy not understand.

1. Given diameter D and length of arc L

; dojina jordi ;
segment height ; central kut .

2. Dani diameter D and dovzhina chordi X

; arc dovjina;
segment height ; central kut .

Oskіlki chord dіlit colo into two segments, the price is not one, but two decisions. Schob otrimatie to each other, it is necessary to use the formulas pointing in the direction to replace the cut α on the cut.

3. Given the diameter D and the central cout φ

; arc dovjina;
dojina jordi ; segment height .

4. Dany diameter D and height of segment H

; arc dovjina;
dojina jordi ; central kut .

6. Given the arc L and the central cout φ

; diameter;
dojina jordi ; segment height .

8. Given a chordi genius X and a central cout φ

; dogina arc ;
diameter; segment height .

9. Dany of the chordi X and the height of the H segment

; dogina arc ;
diameter; central kut .

10. Given the central cut φ і height of the segment H

; diameter ;
arc dovjina; dojina jordi .

Dear reader, I don’t think I’m missing two options:

5. Given an edge of an arc L and an edge of a chordi X

7. Dany of the arc L and the height of the H segment

There are two irrelevant issues, if there is no solution, it is possible to write down the formulas at the viewer. And the zavdannya is not the same anyway. For example, you є have a flat preparation of the L-level and you want to bend it so, the new level became X (for the height became H). What diameter should you take the frame (crossbar)?

The zavdannya price is to be raised before the razvyazannya ryvnyan:
; - for option 5
; - Variant 7
I want the stench not to be scanned analytically, the protest is easy to scan in a programmatic way. And I know how to take this program: on the site itself, for the first time. All those who I do tell you to do it in a microsecond.

To expand the picture of the dodamo to the results of ours, count up to the number of the stake and three values ​​of the area - stake, sector of that segment. (We can help even when calculating the mass of all round and round details, but even in the approximate statistics.)

additional circumference;
cola area ;
sector area ;
area of ​​the segment ;

Once again, I’ll guess again about the idea of ​​absolutely no kostevoy programs, as a vison of all the re-insurance of the calculation, you are aware of the need for zgaduvati, which is also arctangent and de yogo shukati.

The formula for knowing how to finish the arc of a stake is simple, and even more often, on important DI-type experiences, such zavdannya is created, as it is ill-fated to see without storing. It is also necessary for the nobility to fold international standardized tests, for example, SAT and others.

Why should you buy a stake arc?

The wiggle's formula is as follows:

l = πrα / 180 °

She is a skin from the elements of the formula:

• π is the number of Pi (a constant value, which is expensive ≈ 3.14);
• r is the radius of the cola;
• α - the size of the kuta, which spirals the arc (central, but not inscribed).

It can be seen that we must solve the problem, in the minds of the blame r і α. It is hard to know two values ​​without qih.

Yakim rank vivoditsya tsya formula і why so viglyadaє?

Everything is even easier. Become zealous, as if put 360 ° on the banner, and put two on the day before. It is also possible α Do not overdo it in the fraction, just write it with a multiple sign. All in all, you can allow yourself, that the gift of the element will be worthy of the number. Todi zalny viglyad will become like this:

l = (2πr / 360 °) × α

Just for the sake of quickness, they speed up 2 and 360 °. And now, if you are amazed, then you can remember the formula of the dozen of all stake, but you can 2πr. Everything can be stored in 360 °, so there is a 360-degree fit. Let's multiply by a number α, Tobto for that bit of "shmatkiv pie", as we need. But all of it seems that the number (that is, the dinner of all the cola) cannot be extended by a degree. Well, how can such a person be robbed? Name, as a rule, the degree will speed up from the degree of the central kuta, tobto α. The idea is to become overwhelmed, and the result is to come up with a final result.

Tsim can explain to those for whom the arc of the stake is such a rank and such a viglyad.

The butt of the average folding due to the given formula

Umova: Є colo with a radius of 10 centimeters. Set the angle of the central cut to 90 °. To know a dozen of the arc of a stake, I am done with a tsim kut.

Solution: l = 10? × 90 ° / 180 ° = 10? × 1/2 = 5?

Type: l = 5π

So much as possible, the radial world of kuta was given to replace the degree approach. At the same time, it’s not easy to play, and even once it became easy. To convert the radial world into degrees, you need to multiply the number by 180 ° / π. Now, you can now submit a replacement α I will start a combination: m × 180 ° / π. De m - tse radianne meaning. A dal 180 and a number π To speed up and walk, the formula is forgiven, yak viglyadє by the next rank:

• m - radianna mira kuta;
• r is the radius of the cola.

A handful of items are saved on the site between the stake and the surrounding area. Schob poachit qiu rіznitsyu, enough to look, chim є offended fіguri. There is an unlimited number of points in the area, which can be expanded on the road from the central single point. Ale, if there is a lot of storage from the inner space, then there is no way to lay it down. Walk around, where there is a colo and a colo, that is surrounded by that (o-circle), and an unlimited number of dots, that are in the middle of a cola.

For be-such a point L, how to lie on a number, equal to OL = R. (Dovzhina vіdrizka OL dorіvnyu radіusu cola).

Відрізок, which is from the two points of the stake, є її chordium.

Horda, go straight through the center of the stake, є diameter cola (D). The diameter can be calculated using the following formula: D = 2R

Dovzhina circle calculated by the formula: C = 2 \ pi R

Stake area: S = \ pi R ^ (2)

Arc stake to be called that її part, yaka roztashovutsya between two dots. Two points start two arcs of a stake. The chord CD tightens the two arcs: CMD and CLD. However, the jordi contract the same arcs.

Central kut to be called such a kut, which is located between two radii.

Dovzhinu arc you can know behind the formula:

1. Vikoristovyuchi degree turn: CD = \ frac (\ pi R \ alpha ^ (\ circ)) (180 ^ (\ circ))
2. Vikoristovuchi radialny zhіd: CD = \ alpha R

The diameter, which is perpendicular to the chord, extends the chord and the arcs are pulled together by it.

Whenever AB chordi and CD cola may peretin at point N, then create different chords, split by point N, equal to yourself.

AN \ cdot NB = CN \ cdot ND

Stosovno cola

Stosovno cola It is accepted to be called a straight line, for which є has one backward point from the colo.

There are two sleeping points near the straight line, they call sichucho.

I would like to draw a radius at the point of the torch, and it will be perpendicular to the point of the stake.

We will carry out two exact points to our stake. You see, when the dots grow one by one, and the center of the stake grows on the bisectrix kuta with the top at the center of the point.

AC = CB

Now we will carry out the exact same way to the point from our point. Otrimaimo, so the square of the house is similar to the same as it is to the last part.

AC ^ (2) = CD \ cdot BC

You can add a new one: add a whole add-on of the first one to the last part of the day.

AC \ cdot BC = EC \ cdot DC

Kuti in number

Degree of entering the central kut and arc, yaku to spiral, equal.

\ angle COD = \ cup CD = \ alpha ^ (\ circ)

Inscriptions kut- Tse kut, the top of which is to be found on the kolі, and the sides take revenge on the chordi.

It is possible to calculate it, having known the size of the arc, some fragments of the previous half of the arc.

\ angle AOB = 2 \ angle ADB

Yaky spiral on a diameter, inscribed kut, straight.

\ angle CBD = \ angle CED = \ angle CAD = 90 ^ (\ circ)

The inscribed kuti, which spiral on one arc, is the same.

Inscribed kuti based on the same chord, the same sum is available 180 ^ (\ circ).

\ angle ADB + \ angle AKB = 180 ^ (\ circ)

\ angle ADB = \ angle AEB = \ angle AFB

On one number there are the tops of the tricycles with the same kuts and the given basis.

The cut with the top of the middle of the stake and the seams between two chords is the same half of the sum of the core values ​​of the arcs of the stake, which polarize in the middle of the given vertical cut.

\ angle DMC = \ angle ADM + \ angle DAM = \ frac (1) (2) \ left (\ cup DmC + \ cup AlB \ right)

The cut with the top is the posture of the number of gussets between the two, the same half of the difference in the cut-off values ​​of the stake arcs, which are halfway between the middle of the cut.

\ angle M = \ angle CBD - \ angle ACB = \ frac (1) (2) \ left (\ cup DmC - \ cup AlB \ right)

Fitted colo

Fitted colo- Tse colo, why should the sides of the bagatokutnik be stuck.

At the point, the bisectors of the bagatokutnik are changing, the center is being developed.

The circle can be inscribed above the skin polygon.

The area of ​​the bagatokutnik with the inscribed stake is behind the formula:

S = pr,

p - napіvperimeter bagatokutnik,

r is the radius of the inscribed stake.

Zvidsy viplya, the radius of the inscribed stake is delivered:

r = \ frac (S) (p)

Sumi dovzhin of the other sides will be the same, as the number is inscribed in the opukli chotirikutnik. I navpaki: in the opukli chotirikutnik, colo will fit in, as in the new sumi dozhin of the other sides to the same.

AB + DC = AD + BC

For any tricycle it is possible to enter a number. Leave one one. At the point where the bisectors of the inner cuts of the figuri are deformed, there is the center of the inscribed stake.

The radius of the inscribed stake is calculated according to the following formula:

r = \ frac (S) (p),

de p = \ frac (a + b + c) (2)

Described colo

If it is colo to pass through the skin top of the bagatokutnik, then it is taken to nazivati described by the bagatokutnik.

At the point of overflow of the middle perpendiculars of the sides of the figuri, there will be the center of the described stake.

Radius can be known by counting the yak radius cola, yak is described by the tricutnik, which is designated as three peaks of the bagatokutnik.

Є taka umova: it is possible to describe closely the chotirikutnik deprived of it, as the sum of the other huts on the road 180 ^ (\ circ).

\ angle A + \ angle C = \ angle B + \ angle D = 180 (\ circ)

One can describe a bile of a trikutnik, and one, moreover, one. The center of such a stake will be seamed at the points, the middle perpendiculars of the sides of the tricycle are deconstructed.

The radius of the described stake can be calculated by the formulas:

R = \ frac (a) (2 \ sin A) = \ frac (b) (2 \ sin B) = \ frac (c) (2 \ sin C)

R = frac (abc) (4 S)

a, b, c - Dovzhini side tricutnik,

S - the area of ​​the tricycle.

Ptolemy's theorem

Nasamkinets, Ptolemy's theorem is understood.

Ptolemy's theorem is to deduce that there are more diagonals in the same sum of creations of the other sides of the inscribed chotirikutnik.

AC \ cdot BD = AB \ cdot CD + BC \ cdot AD

Zavdannya 10 (ODE - 2015)

At the number of center O, point A and B are equal to AOB = 18 °. Dovzhina of the lesser arc of the AB road 5. Know the dvina of the larger arc of the stake.

Decision

∠ AOB = 18 °. All colo become 360 ​​°. Tom ∠ AOB becomes 18/360 = 1/20 stake.

Otzhe, і mensha arc AB becomes 1/20 of the whole stake, so the arc is great - tse part, tobto. 19/20 cola.

1/20 of the number of additional arcs, which are suitable for the road 5. Todi of the increase of the large arcs are 5 * 19 = 95.

Zavdannya 10 (ODE - 2015)

At the number of center O points A and B so that AOB = 40 °. Dovzhina of the smallest arc AB road 50. Know the dvina of the larger arc of the stake.

Decision

∠ AOB = 40 °. All colo become 360 ​​°. Tom ∠ AOB becomes 40/360 = 1/9 stake.

Otzhe, і mensha arc AB becomes 1/9 of the whole stake, to that the arc is great - tse part, tobto. 8/9 cola.

1/9 of the number of additional arcs, for the road 50. Todi of the increase of the larger arcs for the road 50 * 8 = 400.

View: 400.

Zavdannya 10 (DIA - 2014)

Dovzhina khordi cola road 72, and go to the center of the cola to the cola road 27. Know the diameter of the cola.

Decision

For the theorem of Pyphagoras from the rectangular tricycle AOB we can see:

AO 2 = OB 2 + AB 2,

AO 2 = 27 2 +36 2 = 729 +1296 = 2025,

Todi door diameter 2R = 2 * 45 = 90.

Zavdannya 10 (DIA - 2014)

Point O is the center of the stake, on which points A, B and C lie. Vidomo, ABC = 134 ° and ∠OAB = 75 °. Know the BCO cut. Give it in degrees.

A part of a figuri, a yak set up a colo, a point of a ryvnoviddalene, is called an arc. Just from the point to the center of the stake, make changes to the points that will cross the ends of the arc, if the central kut is established.

Viznachennya dozhini arc

Get ready for this formula:

de L is the arc's length, π = 3.14, r is the radius of the stake, α is the central cut.

L

3.14 x 10 x 85

14,82

View:

Dovzhina arc stakes are 14.82 centimeters long.

In the elementary geometries, there is a growing number of colas that are roasted in two different dots. At the practice, virishuvati zavdannya z valueїї doginie Engineers and architects often have to finish off some geometrical elements of widespread extensions in popular designs.

Mabut, first, in front of them there was a tse of zavdannya, boules of old-time architects, as the parameter for setting up crypts, which was widely used to cross the walls between the supports in round, everyday life. If you respectfully admire the masterpieces of ancient Greek, ancient and especially Arabian architecture, which have gone down to our days, then it is possible to note that in these arc designs and crypts are created superbly often. The creation of the contemporary architects in them is not such a bagat, ale and geometric elements є, it’s very obvious, but in them.

Dovzhin rіznykh arcs it is necessary to repair when equipped with automobiles and tracks, as well as autodromes, and in case of accuracy and accuracy, there is a lot in which to lay a safety deposit. On the right, there are a lot of turns of highways from the point of view of geometry є the arcs themselves, and behind the collapse along them into the transport they pour in different physical forces. The parameters їх resultant are rich in which they begin with a pre-arc arc, as well as with a central cut and radius.

The designers of machines and mechanisms are required to calculate the number of additional arcs for the correct and accurate arrangement of the storage parts of the small units. In the given kind of pardons in rosrahunkah, they are cluttered, but it is important that all the details are wrong to interconnect one by one, and the mechanism simply cannot function like that of his creator. Yak butt constructions, but with such geometric elements, like arcs, it is possible to direct the movement of the internal combustion, gearbox, wood and metal parts, body elements of passenger cars and vantage cars.

Arcs to complete the widespread use of medicine, zokrem, and dentistry. For example, the stench is vicious to correct the wrong bite. Correctional elements, which are called braces (or bracket-systems) and may be of the same shape, are prepared from special alloys, and are installed in such a rank, for changing the position of the teeth. Zrozumіlo, so in order for the process to pass successfully, the arcs are guilty, but they are surely rooted. In addition, the arc is even more widely used in traumatology, and, perhaps, with the best butt of the famous Ilizarov’s apparatus, the winners of the Russian lykar in 1951, and it’s superbly successful to get up to the end of the day. Invincible parts of metal arcs, secured with openings, through which special spokes stretch, which are the main supports of all structures.