It is very important to be familiar with the anatomy of a circle and especially the angles within it. This article covers the properties of arc measures, the formula for an arc measure, and how to find it within a geometric context.
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Jetzt kostenlos anmeldenIt is very important to be familiar with the anatomy of a circle and especially the angles within it. This article covers the properties of arc measures, the formula for an arc measure, and how to find it within a geometric context.
There are two important definitions to be aware of:
An arc is the edge of a circle sector, i.e. the edge bounded/delimited by two points in the circle.
Arc length is the size of the arc, i.e. the distance between the two delimiting points on the circle.
If we think of an arc as being the edge between two points A and B on a circle, the arc measure is the size of the angle between A, the centre of the circle, and B.
In relation to the arc length, the arc measure is the size of the angle from which the arc length subtends.
Here are these definitions demonstrated graphically:
Before we introduce the formula for arc measurement, let’s recap degrees and radians.
To convert radians to degrees: divide by and multiply by 180.
To convert degrees to radians: divide by 180 and multiply by.
Here are some of the common angles which you should recognise.
Degrees | 0 | 30 | 45 | 60 | 90 | 120 | 180 | 270 | 360 |
Radians | 0 |
The formula that links both the arc measure (or angle measure) and the arc length is as follows:
Where
We can find the arc measure given the radius and the arc length by rearranging the formula: .
Find the arc measure shown in the following circle in terms of its radius, r.
Using the formula :
We need the arc measure in terms of r, so we need to rearrange this equation:
If we are not given the radius, r, then there is a second method for finding the arc measure. If we know the circumference of a circle as well as the arc length, then the ratio between the arc measure and (or depending on whether you want the arc measure in degrees or radians) is equal to the ratio between the arc length and the circumference.
Where
c is the circumference of the circle
S is the arc length
Find the arc length, x, of the following circle with a circumference of 10 cm.
Using the formula :
Rearranging, we get:
to 3 s.f.
Where
r is the radius of the circle.
S is the arc length.
Finding the arc measure given the circumference and arc length:
Where:
c is the circumference of the circle.
S is the arc length.
An arc measure is the angle from which an arc of a circle subtends.
How to find the measure of an arc: given the radius and arc length, the arc measure is the arc length divided by the radius. Given the circumference, the ratio between the arc measure and 360 degrees is equal to the ratio between the arc length and the circumference.
The arc measure is the arc length divided by the radius.
The arc measure is the arc length divided by the radius.
In geometry, the arc measure is the arc length divided by the radius.
What is segment length?
Segment length is the distance between two points on straight line.
What is the segment area of a circle?
It is the area bound by a chord and the circle's edge.
A line segment that has its endpoints on a circle is called?
Chord.
A chord passing through the center of the circle is called?
Diameter.
Does a chord, apart from a diameter, any other chord splits a circle into a major arc and a minor arc?
Yes.
Is the following property correct?
Equal chords of a circle subtend equal angles at the center.
Yes.
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