The analysis process is as follows:
(1) analysis shows that the length of a diameter is twice that of a radius in the same circle, but if the two radii are not on a straight line, it cannot be said that the two radii are a diameter. So in the same circle, any two radii can form a diameter, which is wrong.
(2) A circle has countless radii and diameters. In the same circle or equal circle, the length of the diameter is twice that of the radius, and the length of the radius is half that of the diameter; A circle is an axisymmetric figure, and any straight line with a diameter is the symmetry axis of the circle, and the circle has countless symmetry axes.
Extended data
The nature of the circle:
1, the circle is an axisymmetric figure, and its symmetry axis is an arbitrary straight line passing through the center of the circle. A circle is also a central symmetric figure, and its symmetric center is the center of the circle.
2. Vertical diameter theorem: the diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.
3. Inverse theorem of vertical diameter theorem: bisect the diameter of the chord (not the diameter) perpendicular to the chord and bisect the two arcs opposite to the chord.
4. The properties and theorems of central angle and central angle.
5. If one of two central angles, two peripheral angles, two sets of arcs, two chords and the distance between the two chords are equal in the same circle or equal circle, their corresponding other groups are equal respectively.
The definition of circle and its related quantities;
1, a graph composed of all points whose distance from a plane to a fixed point is equal to a fixed length is called a circle. A fixed point is called the center of the circle and a fixed length is called the radius;
2. The part between any two points on a circle is called an 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 chord passing through the center of the circle is called the diameter;
3. The angle of the vertex on the center of the circle is called the central angle. The angle where the vertex is on the circumference and both sides intersect with the circle is called the circumferential angle;
4. 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. A circle tangent to all three sides of a triangle is called the inscribed circle of the triangle, and its center is called the heart;
5. There are three positional relationships between a straight line and a circle: there is no separated common point; There are two common * * * points intersecting; The only thing in common between a circle and a straight line is tangency. This straight line is called the tangent of a circle, and this only thing in common is called the tangent point.
6. There are five kinds of positional relationships between two circles: if there is nothing in common, one circle is called outside the other circle and inside it; 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;
7. 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 becomes the generatrix of the cone.