Lingkaran dan Busur Lingkaran - Matematika SMA Kelas XI Kurikulum Merdeka

Introduction

This tutorial focuses on understanding circles and arcs, specifically tailored for high school mathematics students in Indonesia following the Kurikulum Merdeka. It covers the definitions of a circle and an arc, as well as how to calculate the length of an arc using a specific formula. This knowledge is essential for solving various geometry problems and applying mathematical concepts effectively.

Step 1: Understanding Circles

• A circle is defined as the set of all points in a plane that are equidistant from a fixed point known as the center.
• The distance from the center to any point on the circle is called the radius (r).
• Key points regarding circles:
  • The center is typically labeled as point O.
  • The radius can be measured in any unit (centimeters, meters, etc.).

Step 2: Exploring Arcs

• An arc is a part of the circumference of a circle, consisting of all points that lie on the circle between two endpoints.
• Arcs can be either:
  • Open (not forming a complete loop).
  • Closed (forming a complete loop).
• An arc is usually denoted by its endpoints, for example, arc AB.

Step 3: Calculating Arc Length

• The formula to calculate the length of an arc (AB) is given by:

  Length of arc AB = (a/360) * 2πr
  

  where:

  • "a" is the central angle in degrees subtended by the arc at the center of the circle.
  • "r" is the radius of the circle.
  • π (pi) is approximately 3.14.

Example Calculation

1. If the radius of the circle is 5 cm and the central angle is 60 degrees:
   • First, compute the circumference of the entire circle:

     Circumference = 2πr = 2 * 3.14 * 5 = 31.4 cm
     

   • Next, apply the arc length formula:

     Length of arc AB = (60/360) * 31.4 = (1/6) * 31.4 ≈ 5.23 cm
     

Conclusion

In this tutorial, we've learned the basic concepts of circles and arcs, including their definitions and how to calculate the length of an arc using a specific formula. Understanding these concepts is crucial for solving geometry problems in higher-level mathematics. To further your knowledge, practice by calculating arc lengths with varying radii and angles, and explore how these concepts apply in real-world scenarios such as architecture and engineering.