Notes on Circles - Chapter 10

Importance of Circles

• Circles are prevalent in our surroundings.
  • Examples include:
    • Camera lenses
    • Radio knobs
    • Wheels (impossibility of rectangular/triangular wheels)
    • Earth (side view is circular)
• Circles play a significant role in daily life.

Definition of a Circle

• A circle is defined as a collection of points on 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.

Key Terms Related to Circles

• Diameter: A line segment that passes through the center, connecting two points on the circle.
  • Example: Points A and B.
• Chord: A line segment joining two points on the circle, but not necessarily passing through the center.
  • Example: Points M and N.
• Arc: A portion of the circumference of a circle, defined by two endpoints on the perimeter.
  • Example: Arc XY.
• Segment: The area between a chord and the circle, dividing it into two parts.
• Sector: The area between two radii and an arc.
  • Example: Points X and Y define a sector between two radii.

Situations with a Circle and a Line

1. Non-Intersecting Line:

   • No common points between the line and circle.
   • The line is considered non-intersecting.

2. Tangent Line:

   • The line touches the circle at one point (point of contact).
   • The line is considered a tangent.

3. Secant Line:

   • The line intersects the circle at two distinct points.
   • The line is considered a secant.

Summary

• Circles are fundamental shapes with various applications in the real world.
• Understanding the components of circles and their interactions with lines is crucial in geometry.