The properties of a circle include its center (the fixed point), radius , diameter, and circumference. A circle is a line which curves and joins up with itself such that any point on the line is at equal distance from a fixed point.
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properties of a circle: Parts of a circle
Circumference of a circle
Circumference is the length of the curved line forming the circle.
An arc
An arc is a fraction of the circumference made from an incomplete circle.
chord
A chord is any straight line joining two points on the circumference.
Diameter
Diameter is any chord passing through the center of a circle. Diameter is the longest chord that can be drawn in a circle.
segment
A segment is any region enclosed by a chord and an arc. A chord usually divides a complete circle has into two segments. One segment is smaller than the other.
The smaller segment is referred to as the minor segment while the larger one is referred to as the major segment.
When a chord inside the circle makes two equal chords, then the chords are called semi-circle. In other words, a semicircle is a figure created from an area enclosed by an arc and diameter of a circle.
Sector of a circle
Sector of a circle is a two dimensional figure resulting from an area being enclosed by two radii and an arc .
Any pair of radii that joins at an angle inside a circle makes two sectors. the smaller sector is called the minor sector while the bigger sector is known as the major sector.
Angle properties of a circle
Angle subtended by an arc or a chord
Consider the figure below:
The minor arc ABC subtends and angle ADC at the circumference of the circle. Angle ADC is opposite to arc ABC.
If points A and C are joined by a straight line, chord AC or arc ABC subtends angle ADC at the circumference.
consider the figure below:
The same minor arc as describe above subtends angle AOC at the centre of the circle.
Chords AC or arc ABC subtends angle AOC at the center.
The two diagrams can help us investigate properties of angles subtended by an arc or a chord in the same segment at the circumference.
we conclude that:
Angle subtended by the same arc or chord at the circumference, in the same segment are equal
Equal chords or arcs subtends equal angles at the circumference.
Related topics
- sequence of numbers
- Uniform circular motion