Table of Contents
What is Arc in Math?
An arc in mathematics is a segment of a curve, specifically a portion of the circumference of a circle or an ellipse. It is defined by two endpoints and all the points on the curve between them. The length of an arc is typically measured in terms of the angle it subtends at the center of the circle or ellipse.
How to Make an Arc
Creating an arc involves specifying its starting and ending points. Here are the basic steps:
- Draw a Circle or Ellipse: Start by drawing a circle or ellipse. Use a compass for a precise circle.
- Select the Arc Endpoints: Determine the two endpoints on the circumference of the circle or ellipse that will define the arc.
- Draw the Arc: Use a ruler or a protractor to draw the arc, connecting the chosen endpoints.
Types of Arcs
There are different types of arcs based on their measurement:
- Minor Arc: The smaller arc between two points on a circle, covering less than half of the circle’s circumference.
- Major Arc: The larger arc between two points on a circle, covering more than half of the circle’s circumference.
- Semicircle: An arc that spans exactly half of the circle’s circumference.
- Central Angle Arc: An arc subtended by a central angle at the center of the circle.
Solved Examples
Example 1: Consider a circle with a radius of 6 cm. Find the length of a major arc subtended by a central angle of 120 degrees.
Solution:
Therefore, the length of the major arc is 4π cm.
Example 2: Given a semicircle with a diameter of 10 units, calculate the length of the arc.
Solution:
