An arc is a continuous portion of a curve, typically one that is part of the circumference of a circle. Arcs are often used in geometry and engineering to describe the shape of an object or structure, or to specify the path that a moving object should follow. In this article, we will define the term “arc,” provide five examples of arcs, and offer a quiz to test your understanding of this concept.
Definitions:
- Arc: a continuous portion of a curve, typically one that is part of the circumference of a circle.
- Central angle: an angle formed by two radii of a circle that have their endpoints on the circumference of the circle. The arc formed by this angle is a segment of the circumference of the circle.
- Radius: a straight line connecting the center of a circle to a point on the circumference of the circle.
- Chord: a straight line connecting two points on the circumference of a circle.
- Arc length: the distance along the arc, measured in the same units as the radius.
Examples:
- A quarter-circle is an arc that is one-quarter of the circumference of a circle. It is formed by a central angle of 90 degrees, and has an arc length equal to one-quarter of the circumference of the circle.
- A semicircle is an arc that is half of the circumference of a circle. It is formed by a central angle of 180 degrees, and has an arc length equal to half of the circumference of the circle.
- An arc that is three-quarters of the circumference of a circle is formed by a central angle of 270 degrees. Its arc length is three-quarters of the circumference of the circle.
- A minor arc is an arc that is smaller than a semicircle. It is formed by a central angle that is less than 180 degrees.
- A major arc is an arc that is larger than a semicircle. It is formed by a central angle that is greater than 180 degrees.
Quiz:
- What is an arc? a. a continuous portion of a curve b. a straight line connecting two points on the circumference of a circle c. a straight line connecting the center of a circle to a point on the circumference of the circle d. an angle formed by two radii of a circle that have their endpoints on the circumference of the circle
- What is a radius? a. a continuous portion of a curve b. a straight line connecting two points on the circumference of a circle c. a straight line connecting the center of a circle to a point on the circumference of the circle d. an angle formed by two radii of a circle that have their endpoints on the circumference of the circle
- What is a chord? a. a continuous portion of a curve b. a straight line connecting two points on the circumference of a circle c. a straight line connecting the center of a circle to a point on the circumference of the circle d. an angle formed by two radii of a circle that have their endpoints on the circumference of the circle
- What is a central angle? a. a continuous portion of a curve b. a straight line connecting two points on the circumference of a circle c. a straight line connecting the center of a circle to a point on the circumference of the circle d. an angle formed by two radii of a circle that have their endpoints on the circumference of the circle
