6. Circles
Exercises
Definitions
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.
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A chord is a segment that connects two points on the circumference of a circle.
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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.
![Circle related definitions: central point, radius, perimeter, tangent, diameter, arc, chord.](https://peda.net/qis/2022-2023/mathematics/maths-all/o2kljpa/6-ympyr%C3%A4/m%C3%A4%C3%A4ritelmi%C3%A4/7:file/photo/d0f9befd1f519571f6de2ac10291235a13171071/6_circle-related-definitions.png)
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.
![Areas of a circle: sector and segment](https://peda.net/qis/2022-2023/mathematics/maths-all/o2kljpa/6-ympyr%C3%A4/m%C3%A4%C3%A4ritelmi%C3%A4/72:file/photo/d21759de72f02dab3714e70f08e55afdbd8ce0c5/6_circle-areas.png)
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$]]