What is Arc in Math?
In the realm of mathematics, an arc is a gracefully curved segment along the periphery of a geometric figure, frequently associated with circles or ellipses. It is not merely a line; rather, it is defined by two distinctive endpoints and encompasses all the points that elegantly trace the curve between these endpoints. The measurement of an arc is often expressed in terms of the angle it forms at the center of the circle or ellipse.
How to Make an Arc
Crafting an arc is akin to painting a stroke of elegance onto the canvas of geometry. Here’s a step-by-step guide:
- Draw a Circle or Ellipse: Embark on your geometric journey by sketching a circle or ellipse, and for precision, consider wielding a compass as your artistic tool.
- Select the Arc Endpoints: Much like an artist deciding on the pivotal points in a masterpiece, determine two distinct endpoints on the circumference of the circle or ellipse that will serve as the defining anchors of your arc.
- Draw the Arc: With the decisiveness of a brushstroke, use a ruler or protractor to draw the arc, gracefully connecting the chosen endpoints and letting the curve unfold.
Types of Arcs
Arcs, like the nuanced strokes of a painter’s brush, come in various forms:
- Minor Arc: A delicately smaller arc, spanning less than half of the circle’s majestic circumference.
- Major Arc: The grander counterpart, stretching across more than half of the circle’s circumference.
- Semicircle: A perfectly balanced arc, encapsulating precisely half of the circle’s allure.
- Central Angle Arc: An arc influenced by a central angle, emanating a certain radiance from the heart of the circle.
Solved Examples
Example 3: Find the measure of a central angle that subtends a minor arc of length 8 cm in a circle with a radius of 4 cm.
Solution:
Therefore, the central angle measure is 2 radians.