Overview
This lesson covers the main parts of a circle, their definitions, how to name them, and basic example problems involving these parts.
Definition and Naming of a Circle
- A circle is the set of all points in a plane at a fixed distance (radius) from a center point.
- The center of the circle is labeled as point A in the figure.
- Circles are named after their center (e.g., Circle A).
- Radii (plural of radius) are line segments from the center to any point on the circle (e.g., segments AC and AB).
Parts of a Circle
- A radius is a segment with endpoints at the center and a point on the circle; its length is the distance from the center to the circle.
- A chord is a line segment with both endpoints on the circle.
- A diameter is a chord passing through the center; its length is twice the radius.
- Example: If the diameter is 12 cm, the radius is 6 cm.
Special Lines Related to Circles
- A tangent is a line, segment, or ray that touches the circle at exactly one point.
- A secant is a line, segment, or ray that intersects the circle at exactly two points.
- Every chord is part of a secant; every secant contains a chord.
Naming Examples
- The tangent line is named as line l.
- The point of tangency is named as point F.
- The chord in the example is segment BC.
- The secant is line BC or line m.
Example Problems
- Given AB = 2x - 3 and AC = x + 1, set AB = AC to find x, then solve for the radius and diameter.
- In concentric circles (having the same center), if EA = 10 cm and C is the midpoint of AB, then AB = 10 cm, AC = 5 cm, and BD or BC = 5 cm.
- If EB = 2 × 10 + 5 = 25 cm, and ED = 15 cm (from example problem steps).
Key Terms & Definitions
- Circle — Set of all points at a fixed distance from a center in a plane.
- Center — Fixed point from which the radius is measured.
- Radius (radii) — Segment from the center to any point on the circle.
- Chord — Segment with both endpoints on the circle.
- Diameter — Chord passing through the center; equals two radii.
- Tangent — Line touching the circle at exactly one point.
- Secant — Line intersecting the circle at exactly two points.
- Concentric Circles — Circles with the same center.
Action Items / Next Steps
- Review the definitions and properties of each part of a circle.
- Practice naming parts of a circle using given diagrams.
- Solve similar problems involving chords, diameters, tangents, and secants for better understanding.