Tali Busur Lingkaran - Matematika SMA Kelas XI Kurikulum Merdeka

Introduction

This tutorial provides a comprehensive guide on understanding the concept of Tali Busur Lingkaran (Chord of a Circle) as part of the Matematika SMA Kelas XI Kurikulum Merdeka. The tutorial will cover definitions, properties, and practical applications, ensuring a solid grasp of this essential mathematical concept.

Step 1: Understanding Tali Busur Lingkaran

• Definition: A Tali Busur Lingkaran is a line segment that connects two points on the circumference of a circle.
• Key Characteristics:
  • It is the shortest distance between the two points on the circle.
  • It can be visualized as cutting through the circle, unlike a Busur (Arc), which follows the circle's curvature.

Step 2: Identifying Points on the Circle

• Selecting Points: Choose any two points on the circumference of the circle. Label them as A and B.
• Drawing the Chord: Draw a straight line connecting points A and B. This line represents the Tali Busur Lingkaran.

Step 3: Calculating the Length of the Chord

• Formula: The length of the chord can be calculated using the formula:

  [ L = 2 \times r \times \sin\left(\frac{\theta}{2}\right) ]

  Where:

  • ( L ) = Length of the chord
  • ( r ) = Radius of the circle
  • ( \theta ) = Central angle subtended by the chord at the center of the circle (in radians)

• Practical Tip: Ensure that you convert degrees to radians if necessary by using the formula:

  [ \text{radians} = \frac{\pi}{180} \times \text{degrees} ]

Step 4: Exploring Properties of Chords

• Central Angles: The central angle is twice the angle subtended by the chord at any point on the circle's circumference.
• Equal Chords: Chords that are equal in length subtend equal angles at the center of the circle.

Step 5: Real-World Applications

• Architecture and Engineering: Chords are often used in designing arches and circular structures.
• Navigation and Surveying: Understanding distances and angles in circular paths is crucial for accurate mapping.

Conclusion

In this tutorial, we explored the concept of Tali Busur Lingkaran, including its definition, calculation of its length, and properties. Understanding these principles is essential for further studies in geometry and mathematical applications. As a next step, consider practicing problems related to chords and arcs to reinforce your understanding.