What is the formula for calculating the radius of a circle?

What is the formula for calculating the radius of a circle?

Are you looking for area or perimeter or volume? This is his related formula [definition of circle]
Geometry said: the distance from the plane to the fixed point is equal to the fixed length of all the points of the graph is called a circle. The fixed point is called the center of the circle, the fixed length is called the radius
Trajectory theory: a moving point on the plane with a certain point as the center and a certain length as the distance is called a circle
Set theory: a set of points whose distance to a fixed point is equal to a fixed length is called a circle
Correlation of circles
PI: the ratio of the circumference length to the diameter length of the circle is called PI. The value is 3.14159265358979323846 It is usually expressed by π and its approximate value is 3.1416
Arc chord: the part between any two points on a circle is called arc, or arc for short. The arc larger than semicircle is called superior arc, and the arc smaller than semicircle is called inferior arc. The line segment connecting any two points on a circle is called chord. The chord passing through the center of the circle is called diameter
Center angle and circumference angle: the angle where the vertex is on the center of the circle is called the center angle. The angle where the vertex is on the circle and its two sides have another intersection with the circle is called the circumference angle
Inner and outer center: 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. The circle tangent to the three sides of the triangle is called the inscribed circle of the triangle, and its center is called the inner center
Sector: on a circle, a figure enclosed by two radii and an arc is called a sector. The side expansion of a cone is a sector. The radius of the sector becomes the generatrix of the cone
Letter representation of circle and its related quantity
Circle - ⊙ radius - R arc - diameter - D
Sector arc length / conical bus - L perimeter - C area - S
Location relationship between circle and other figures
The location relationship between circle and point: take the 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), P is outside ⊙ o, Po > R; P is on ⊙ o, Po = R; P is in ⊙ o, Po < R
There are three kinds of positional relations between a line and a circle: no common point is the separation; two common points are the intersection; a circle and a line have a unique common point as the tangent, which is called the tangent of the circle, and this unique common point is called the tangent point. Take the line AB and the circle O as an example (let op ⊥ AB be in P, then Po is the distance from AB to the center of the circle): AB and ⊙ o are separated, Po > R; Ab and ⊙ o are tangent, Po = R; Ab and ⊙ o intersect, Po < R
There are five kinds of positional relations between two circles: if there is no common point, a circle outside the other circle is called exocentric and inside is called introcentric; if there is a unique common point, a circle outside the other circle is called circumscribed and inside is called inscribed; if there are two common points, it is called intersection. The distance between the centers of two circles is called center distance. The radii of two circles are R and R respectively, and R ≥ R, The center distance of the circle is p: outward P > R + R; circumscribed P = R + R; intersected R-R < p < R + R; inscribed P = R-R; included P < r-r
[plane geometric properties and theorems of circles]
Basic properties and theorems of circles
Circle determination: three points not on the same line determine a circle
Symmetry property of circle: a circle is an axisymmetric figure, and its axis of symmetry is any straight line passing through the center of the circle. A circle is also a centrosymmetric figure, and its center of symmetry is the center of the circle
Inverse theorem: the diameter of the bisector (not the diameter) is perpendicular to the chord and bisectors the arc of the chord
On the properties and theorems of circle circumference angle and center angle
In the same circle or equal circle, if one group of quantities of two center angles, two circumference angles, two arcs and two strings is equal, then the other groups of quantities corresponding to them are equal respectively
The circular angle of an arc is equal to half of its central angle
The circle angle of diameter is right angle. The circle angle of 90 degrees is diameter
Properties and theorems of circumscribed circle and inscribed circle
A triangle has a unique circumscribed circle and an inscribed circle. The center of the circumscribed circle is the intersection of the vertical bisectors of each side of the triangle, and the distance to the three vertices of the triangle is equal; the center of the inscribed circle is the intersection of the bisectors of each angle of the triangle, and the distance to the three sides of the triangle is equal
Properties and theorems of tangent
The tangent of a circle is perpendicular to the diameter passing through the tangent point; a line passing through one end of the diameter and perpendicular to the diameter is the tangent of the circle
Tangent theorem: the line passing through the outer end of the radius and perpendicular to the radius is the tangent of the circle
The properties of tangent: (1) the line passing through the tangent point perpendicular to the radius is the tangent of the circle. (2) the line passing through the tangent point perpendicular to the tangent must pass through the center of the circle. (3) the tangent line of the circle is perpendicular to the radius passing through the tangent point
Tangent length theorem: from a point outside the circle to the length of two tangents, etc
Calculation formula of circle
1. Circumference of circle C = 2 π r = π D 2. Area of circle s = π R2 3. Sector arc length L = n π R / 180
4. Sector area s = n π R2 / 360 = RL / 2 5. Side area of cone s = π RL