Definitions

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A circle is a two-dimensional pattern that consists of all the points that are within a certain distance from a given central point. The circle is named after its central point.

Circle - related definitions

The perimeter of a circle is a plane curve that consists of all the points that have the same distance from the circle's centre.
The radius of a circle is a segment that connects the centre of the circle with a point at its perimeter.
A chord is a segment that connects two points on the circumference of a circle.
The diameter is the chord that passes through the circle's central point.
A tangent is a line that flanks a circle at one point.
Two points on the perimeter of a circle divide its circumference into two arcs.

Parts of a circle O

radius OC
diameter AB or chord DE
chord DE
arc CB

Areas of a circle

A sector is an area of a circle bounded by two radii.
A sector's central angle [[$\alpha$]] has its vertex at the circle's centre.
A chord divides the circle into two segments.

Since each chord divides a circle into two segments, it is important to clearly mark which segment is meant. The same applies to sectors.

The diameter of a circle

The diameter [[$ d $]] of a circle is twice the length of its radius [[$ r $]].
[[$d = 2r$]]

Example 1

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Calculate the length of the diameter O and the magnitude of the reflex angle AOB.

The diameter of the circle [[$ d = 2r = 2 \cdot 23 \text{ cm} = 46\text{ cm}$]].

A round angle is [[$360°$]], which means that [[$\angle$]] AOB[[$= 360° -110° = 250°$]].

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