A circle is a geometric figure, which refers to the set of all points on a plane with a constant distance from a fixed point. This given point is called the center of the circle. The distance as a fixed value is called the radius of a circle. When a line segment rotates once around one of its endpoints on a plane, the trajectory of its other endpoint is a circle. There are countless circles in diameter; A circle has countless axes of symmetry. The diameter of a circle is twice the radius, and the radius of a circle is half the diameter.
When drawing a circle with a compass, the point where the needle tip is located is called the center of the circle, which is generally represented by the letter O. The line segment connecting the center of the circle with any point on the circle is called the radius, which is generally represented by the letter R. The length of the radius is the distance between the two corners of the compass. The line segment passing through the center of the circle and with both ends on the circle is called the diameter, which is generally represented by the letter D.
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 arc opposite to the chord. Inverse theorem: bisecting the diameter of a chord (not the diameter) is perpendicular to the chord and bisecting the arc opposite to the chord.
3. In the same circle or equal circle, if one of two central angles, two peripheral angles, two arcs and two chords has the same quantity, the corresponding other groups are equal.
The angle of the circle the arc subtends is equal to half the angle of the circle it subtends.
5. The circumferential angle of the diameter is a right angle. The chord subtended by a 90-degree circle angle is the diameter.
6. Three points that are not on the same straight line determine a circle.
7. A triangle has a unique circumscribed circle and inscribed circle. The center of the circumscribed circle is the intersection of the perpendicular lines of each side of the triangle, and the distances to the three vertices of the triangle are equal; The center of the inscribed circle is the intersection of the bisectors of the inner angles of the triangle, and the distances to the three sides of the triangle are equal.