Garis Singgung Lingkaran (1) - Pengertian Garis Singgung, Rumus Dasar - Matematika SMP

Introduction

This tutorial provides a clear understanding of the tangent line to a circle, including its definition and basic formulas. This topic is essential for students studying mathematics at the junior high school level, as it lays the foundation for more advanced geometric concepts.

Step 1: Understanding the Tangent Line

• A tangent line to a circle is a straight line that touches the circle at exactly one point.
• This point of contact is called the point of tangency.
• Key properties of tangent lines:
  • They are perpendicular to the radius drawn to the point of tangency.
  • A circle can have an infinite number of tangent lines, but each tangent line will only touch the circle at one point.

Step 2: Identifying the Circle and Radius

• To define a tangent line, you need to identify the following:
  • The center of the circle (point O).
  • The radius (line segment from the center to any point on the circle).
• Use the formula to find the radius:
  • If the radius is given as 'r', the circle's equation can be expressed as:

    (x - h)² + (y - k)² = r²
    

    where (h, k) is the center of the circle.

Step 3: Drawing the Tangent Line

• Follow these steps to draw the tangent line:
  1. Draw the circle using a compass or a drawing tool.
  2. Mark the center (O) and a point (T) on the circumference where you want to draw the tangent.
  3. Draw the radius OT.
  4. At point T, draw a line that is perpendicular to OT. This line is your tangent line.

Step 4: Using the Tangent Line Formula

• The slope of the tangent line can be derived from the radius.
• If the coordinates of the center are (h, k) and the tangent point is (x, y), the slope of the radius OT is:

  m_radius = (y - k) / (x - h)
  

• The slope of the tangent line (m_tangent) will be the negative reciprocal:

  m_tangent = -1/m_radius
  

• Use this slope to write the equation of the tangent line in point-slope form:

  y - y₁ = m_tangent(x - x₁)
  

  where (x₁, y₁) is the point of tangency (T).

Conclusion

Understanding tangent lines is crucial in geometry. Remember:

• A tangent touches the circle at one point and is perpendicular to the radius at that point.
• Use the radius to derive the slope of the tangent line.
• Practice drawing tangent lines and using the formulas to solidify your understanding.

Next, you can explore more complex problems involving tangents or look into secants and their differences from tangents to deepen your knowledge of circle geometry.