In this publication, we will consider the definition and properties of one of the main geometric shapes – the circle. We also give formulas with which you can find its radius, diameter, perimeter and area (total and sectors).
Definition of a circle
Circle is a set of points on the plane, bounded (i.e., lying inside the circle). In the image below, everything that is shaded in turquoise is a circle.
Circle sector – the area inside the circle, which is formed by two radii and an arc between them.
circle segment – the area formed as a result of dividing the circle by a chord, which in turn is part of secant (straight line) intersecting the circle.
- AB – secant;
- CD – a chord (a segment connecting any two points on a circle).
Circle Properties
Property 1
The center of the circle coincides with the center of the circle bounding it. Most often, denoted by the letter O.
Property 2
Circle radius (R) is, among other things, the radius of the boundary circle. This is a segment connecting the center of the circle with any point lying on its boundary, i.e. on the circle.
The chord passing through the center of the circle is called diameter (d).
Property 3
The perimeter of a circle is equal to the length of its bounding circle.
Property 4
A circle, compared to other figures, has the largest area for a given perimeter.
formula
1. Circle perimeter (L):
2. Circle radius (R):
3. Circle diameter (d):
4. Circle area (S):
5. Sector area (S):
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