circle

definition

The definition of a circle is 2.

First of all, a point set whose distance from a plane to a fixed point is equal to a fixed length is called a circle.

Second, a line segment on the plane rotates 360 around one end, leaving a track called a circle. Generally, a circle is folded in half on a straight line and completely coincides. After folding, the point where these creases intersect is called the center of the circle, represented by the letter O, the line segment connecting the center of the circle with any point on the circle is called the radius, represented by the letter R, the line segment passing through the center of the circle with both ends on the circle is called the diameter, represented by the letter D, the center of the circle determines the position of the circle, and the radius and diameter determine the size of the circle. In the same circle or equal circle, the radii are all equal and the diameters are all equal. The diameter is twice the radius, and the radius is 1/2 of the diameter.

Represented by letters is: d=2r or r=d/2. The ratio of the circumference to the diameter and length of a circle is called pi, which is an infinite cycle decimal. It is usually expressed by π=3. 14 15926535 ... In practical application, we only take its approximate value, namely π ≈ 3.65435.

Arc chord: the part between any two points on the circle is called arc, or simply arc. An arc larger than a semicircle is called an upper arc, and an arc smaller than a semicircle is called a lower arc. A line segment connecting any two points on a circle is called a chord. The longest chord in a circle is the diameter.

Central angle and central angle: the angle of the vertex on the center of the circle is called the central angle. The angle at which the vertex is on the circumference and both sides intersect with the circle is called the circumferential angle.

Inner heart and outer heart: the circle tangent to all three sides of a triangle is called the inscribed circle of this triangle, and its center is called the inner heart. The circle passing through the three vertices of a triangle is called the circumscribed circle of the triangle, and its center is called the outer center of the triangle.

Sector: On a circle, the figure enclosed by two radii and an arc is called a sector. The development diagram of the cone is a sector. The radius of this sector is called the generatrix of the cone.

Letter representation of correlation between circles

Circle-⊙ Radius -R or R (letter indicated by the radius of the outer circle of a circle) Arc-⌒ Diameter -D

Sector arc length/conic generatrix -l perimeter -c area-positional relationship between S circle and other figures: positional relationship between circle and point: Take point P and circle O as an example (let p be a point, then PO is the distance from the point to the center of the circle), where P is outside ⊙O and PO > R；; P on ⊙O，po = r； P is within ⊙O, and po < r.

There are three positional relationships between a straight line and a circle: there is no separated common point; There are two common points intersecting, and this straight line is called the secant of the circle; A circle and a straight line have a unique common tangent point. This straight line is called the tangent of the circle, and this unique common point is called the tangent point. Take straight line AB and circle O as examples (let OP⊥AB be in P, then PO is the distance from AB to the center of the circle): AB is separated from ⊙O, and po > r；; AB is tangent to ⊙O, po = r；; AB and ⊙O intersect, po < r.

There are five kinds of positional relations between two circles: if there is nothing in common, one circle is called external separation and internal inclusion outside the other; If there is only one common point, a circle is called circumscribed by another circle and inscribed by another circle; There are two things in common called intersection. The distance between the centers of two circles is called the center distance. The radii of the two circles are R and R respectively, and R≥r, and the center distance is P: outward separation P > R+R; Circumscribed p = r+r; Intersection r-r < p < r+r; Inner cut p = r-r; Include p