exercises om major
and minor arc
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Arc Of A Circle
In these lessons, we will learn
- the arc of a circle
- the central angle
- the arc measure
- the arc length formula when the arc measure is given in degrees
- the arc length formula when the arc measure is given in radians
- how to calculate the arc length using the arc length formula
Arc of a Circle
An arc is any connected part of the circumference of a circle.
In the diagram above, the part of the circle from M to N forms an arc. It is called arc MN.
An arc could be a minor arc, a semicircle or a major arc.
- A semicircle is an arc that is half a circle.
- A minor arc is an arc that is smaller than a semicircle.
- A major arc is an arc that is larger than a semicircle
Central Angle
A central angle is an angle whose vertex is at the center of a circle.
In the diagram above, the central angle for arc MN is 45°.
The sum of the central angles in any circle is 360°.
Arc Measure
The measure of a semicircle is 180°.
The measure of a minor arc is equal to the measure of the central angle that intercepts the arc. We can also say that the measure of a minor arc is equal to the measure of the central angle that is subtended by the arc. In the diagram below, the measure of arc MN is 45°.
The measure of the major arc is equal to 360° minus the measure of the associated minor arc.
The following video shows how to identify semicircle, minor arc and major arc and their measures.
