Circle Vocabulary
A circle is the set of all points equidistant from a center. Before studying circle theorems, you need fluency with the vocabulary: radius, diameter, chord, secant, tangent, and arc.
Introduction
Circles appear everywhere — wheels, coins, orbits, clocks. This lesson establishes the precise language you'll use throughout Unit 10 to describe every line, segment, and region related to a circle.
Past Knowledge
Points, lines, segments (1.1). Distance formula (1.2.4). Angles.
Today's Goal
Master circle vocabulary: radius, chord, diameter, secant, tangent, arc.
Future Success
Central & inscribed angles (10.1.2–10.1.4), tangent theorems (10.2.1).
Key Concepts
Line & Segment Terms
| Term | Definition |
|---|---|
| Center | The point all circle points are equidistant from |
| Radius () | Segment from center to circle; |
| Diameter () | Chord through the center; longest chord; |
| Chord | Segment with both endpoints on the circle |
| Secant | Line that intersects the circle at exactly 2 points |
| Tangent | Line that touches the circle at exactly 1 point (the point of tangency) |
Arc & Region Terms
| Term | Definition |
|---|---|
| Minor Arc | Shorter arc between two points; measure < 180° |
| Major Arc | Longer arc; measure > 180°; named with 3 letters |
| Semicircle | Arc = 180°; half the circle; cut by a diameter |
| Sector | “Pizza slice” — region between two radii and an arc |
| Segment (of circle) | Region between a chord and its arc |
Circle Anatomy
All key circle parts labeled on one diagram
Worked Examples
Radius-Diameter Relationship
A circle has radius 7. Find its diameter.
d = 14
Chord vs. Secant
AB is a chord. Is it also a secant? Is it a diameter?
A chord is a segment; if extended to a line, it becomes a secant. So the line through A and B is a secant.
A chord is a diameter only if it passes through the center.
Every chord defines a secant line, but is a diameter only if it passes through center.
Naming Arcs
Points A, B, C are on circle O. Minor arc AB = 110°. Name the major arc and find its measure.
Major arc = (use 3 letters to distinguish from minor)
Major arc ACB = 250°
Common Pitfalls
Radius vs. Diameter
Always check if a problem gives radius or diameter. Mixing them up doubles or halves your answer.
Minor Arc Uses 2 Letters, Major Arc Uses 3
is the minor arc. The major arc must include a third point on the longer path to avoid ambiguity.
Real-Life Applications
Wheels & Gears
Every wheel has a center (axle), radius (spoke), and the tire traces a circular path. Gears use the chord-tangent relationship for teeth meshing.
Radar & Sonar
Radar screens show circles centered on the antenna. Objects appear as points at specific radii and arc positions.
Practice Quiz
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