What is the relationship between the position of the circle and the circle, and how can it be learne

There are five kinds of positional relations between circles and circles, intersecting, distancing, intanguling, intanguling, and containing. I believe that the landlord doesn't really understand these location relationships in his head, but he can't use them. I'm sure you hate rote memorization toor1-r2|with |o1o2|The size of the circle to judge the position of the relationship relation, because I also hate it.

This kind of question is nothing more than this practice, but it is not necessary to remember it firmly, as long as you must remember the diagram of these five kinds of position relationships, and then make a little judgment. For example, there is a problem that gives the equation of two circles x 2 + y 2 = 9, and (x + 4) 2 + y 2 = 1 to ask you what is the relationship between the positions of the two circles, first of all, the first step is to figure out the [center coordinates] of the two circles, that is, (0,0) and (-4,0). Then, there is the size of the [radius] of the two circles, i.e., 3 and 1.

These two key quantities can be derived from equations and are not difficult. Next, the distance between the two centers of the circle is obtained from the [center of the circle] coordinates, and the distance between the two centers is obtained from the formula of the distance from the point to the straight line, and the distance between the centers of the two circles is 4. Next is the sum of the distance between the two radii, which is 3+1=4

See, the distance between the two centers and the sum of the distances between the two radii are both four, so these two circles are inscribed. In other words, this kind of problem, find the distance between the center of the circle, find the sum of the radius, compare the distance between the center of the circle and the sum of the radius, and whoever is larger and who is smaller means what kind of positional relationship corresponds. I won't go into detail about who is big and who is small corresponds to what kind of position relationship, in particular, the landlord needs to embody this algebraic operation in geometry, that is, you should use a good scratch paper when you calculate the problem, draw a diagram, this is analytical geometry after all, drawing is a good assistant, I have never deliberately memorized five kinds of |r1-r2|with |o1o2|The formula of the size relationship will still solve this kind of problem, and the trick is to draw a diagram and then analyze the topic.

I hope the landlord can give my opinion

Containing, extangling, intersecting, intangible, distancing, geometric inscriptions are better.

The only and best way is to do the problem to death.

The positional relationship between circles includes detachment, incision, intangent, intersection, and inclusion. A circle refers to a closed curve formed by rotating a moving point at a certain length at a certain distance in a plane. A circle has an infinite number of dots.

A circle is an axisymmetric, center-symmetrical figure, and its axis of symmetry is the straight line where the diameter is located.

Methods for judging the relationship between the position of a circle and a circle:

Let the radius of the two circles be r and r, and the distance between the centers of the circles is d.

1. If d>r+r, the two circles are separated. The sum of the distances between the centers of the two circles is greater than the sum of the radii of the two circles.

2. If d=r-r, then the two circles are inscribed. The sum of the distances between the centers of the two circles is equal to the difference between the radii of the two circles.

3. If d=r+r, then the two circles are inscribed. The sum of the distances between the centers of the two circles is equal to the sum of the radii of the two circles.

4, if d5, if d

Circles can be represented by sets, and the standard equation for a circle is (x - a) y - b) r. where (a, b) is the center of the circle and r is the radius.

There are five kinds of positional relations between circles, namely: alien, tangent (inscribed and inscribed), intersected, and contained.

The specific method of judgment is the destruction of silver spring:

1. Alienation: the sum of the radii of the two circles, less than the center distance of the circle.

2. Tangent: The sum (difference) of the radii of the two circles is equal to the distance between the center of the circle, which is divided into inward and outward.

3. Intersection: The difference between the center distance of the two circles is greater than the radius, and less than the sum of the radies.

4. Contains: The sum of the distance between the centers of the two circles is less than the difference between the radii of the two circles.

There are five kinds of vertical envy overlay relationships between circles and circles: outward, outward, intersecting, inward, and inclusive.

Let the radius of the two circles be r and r, and the distance between the centers of the circles is d. There are five types of relationships:

1. D>R+R two circles are separated; The sum of the distances between the centers of the two circles is greater than the sum of the radii of the two circles.

2. D=R+R two circles are inscribed; The sum of the distances between the centers of the two circles is equal to the sum of the radii of the two circles.

3. D=R-R two circles are inscribed; The sum of the distances between the centers of the two circles is equal to the difference between the radii of the two circles.

4. D r-r two circles are included; The sum of the distances between the centers of the two circles is less than the difference between the radii of the two circles.

5. D r + r two parks intersect; The sum of the distances between the centers of the two circles is less than the sum of the radii of the two circles.

The nature of the circle: 1. The circle is an axisymmetric figure, and the symmetry axis of Pai Tong is any straight line through the center of the circle. A circle is also a center-symmetrical figure, and its center of symmetry is the center of the circle.

Perpendicular diameter theorem: Bisect the string perpendicular to the diameter of the string, and bisect the 2 arcs of the chord opposite.

The inverse theorem of the perpendicular diameter theorem: the diameter of the bisector chord (not the diameter) is perpendicular to the chord, and the 2 arcs of the bisector chord are opposed.

2. Properties and theorems of circumferential and central angles.

In the same circle or equal circle, if one set of quantities in two central angles, two circumferential angles, two sets of arcs, two strings, and two chord center distances are equal, then the rest of the groups of quantities corresponding to them are equal.

In an identical or equal circle, the circumferential angle of an equal arc is equal to half of the central angle of the circle to which it is opposite (the circumferential angle is on the same side as the central angle of the chord).

The answer is not easy, please give an affirmation.

Positional relations between circles: detached, tangent (inscribed and inscribed), intersected, contained.

The position of the circle to the circle is intersecting. How to judge the position relationship between circles:

1. Let the radius of the two circles be r and r, and the center distance of the circles is d.

There are five types of relationships:

1. D>R+R two circles are separated; The sum of the distances between the centers of the two circles is greater than the sum of the radii of the two circles.

2. d=r+r two circles are inscribed: The sum of the distances between the centers of the two circles is equal to the sum of the radii of the two circles.

3. d=r-r two circles inscribed: The sum of the distance between the centers of the two circles is equal to the difference between the radii of the two circles.

4、d5、d<>

Second, the position relationship between the circle and the circle can also be judged by whether there is a common point:

1. There is no common point, a circle outside another circle is called outside, and inside it is called inclusion.

2. If there is a single common point, a circle outside another circle is called an external incision, and an internal incision is called an internal incision.

3. There are two common points called intersection. The distance between the centers of two circles is called the center distance.

1. The positional relationship between the circle and the circle.

If two circles do not have a common point, then the two circles are said to be separated, and there are two types of separation: external and internal.

If two circles have only one common point, then the two circles are said to be tangent, and tangent is divided into two types: inscribed and inscribed.

If two circles have two common points, then the two circles are said to intersect.

2. Center distance.

The distance between the centers of the two circles is called the distance between the centers of the two circles.

3. The nature and determination of the relationship between the circle and the position of the circle.

Let the radii of the two circles be r and r respectively, and the centroid distance of the circles is d, then.

The two circles are separated from d>r+r

The two circles are inscribed d=r+r

Two circles intersect r-r

The two circles are inscribed d=r-r(r>r).

Two circles contain dr).

1. The positional relationship between circles and circles: outer volume Huai separation, tangent (incision and incision), intersection, and inclusion. In a plane, a closed curve formed by a moving point centered on a hail point and rotated around a certain length is called a circle.

2. There is no common point, a circle outside another circle is called outside, and inside is called inclusion.

3. If there is a single large sail common point, a circle outside another circle is called an external cut, and an inner circle is called an internal cut.

4. Where there are two common points, it is called intersection. The distance between the centers of two circles is called the center distance.