A prominent feature of a circle is that the distance from the center of the circle to all points on the circle is the same, that is to say, the distance from the bystander to the circle where the bystander is located is the same, thus achieving a balanced state. The distance between people and onlookers is the same, which has a sense of security and can achieve the same visual effect.
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Zazie Hoko
The nature of the cycle is as follows:
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.
Vertical diameter theorem: the diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.
Inverse theorem of vertical diameter theorem: bisecting the diameter of a chord (not the diameter) is perpendicular to the chord and bisecting two arcs opposite to the chord.
2. The properties and theorems of central angle and central angle;
In the same circle or in the same circle, if the distance between two central angles, two peripheral angles, two sets of arcs, two chords and one of the two chords is equal, the corresponding other groups are equal.
In the same circle or in the same circle, the circumferential angle of an equal arc is equal to half of the central angle it faces (the circumferential angle and the central angle are on the same side of the chord).
The circumferential angle of the diameter is a right angle. The chord subtended by a 90-degree circle angle is the diameter.
The formula for calculating the central angle is θ = (l/2π r) × 360 =180l/π r = l/r (radian).
That is, the degree of the central angle is equal to the degree of the arc it faces; The angle of a circle is equal to half the angle of the arc it faces.
If the length of an arc is twice that of another arc, then the angle of circumference and center it subtends is also twice that of the other arc.
3. The properties and theorems of circumscribed circle and inscribed circle;
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.
R=2S△÷L(R: radius of inscribed circle, S: area of triangle, L: perimeter of triangle).
The intersection of two tangent circles. (line: a straight line with two centers connected)
The midpoint m of the chord PQ on the circle O. If the intersection point m is the intersection of two chords AB, CD, AC and BD with PQ on X and Y respectively, then M is the midpoint of XY.