Parts of a Circle
Define and distinguish the key parts: center, radius, diameter, chord, secant, tangent, arc (minor/major), semicircle, and central angle. Use these terms precisely in theorems and problems throughout the unit.
A lesson of Geometry, in Circles, about 10 minutes.
By the end of this lesson, you will be able to identify and name all parts of a circle (center, radius, diameter, chord, secant, tangent, arc, central angle, inscribed angle), use correct notation, and apply basic circle relationships.
The Big Idea
A circle is the set of all points in a plane equidistant from a fixed point (the center). Every theorem about circles depends on a precise understanding of its parts. This vocabulary lesson is the foundation for all circle geometry that follows.
Basic Parts
Center ($O$): the fixed point equidistant from all points on the circle. The center is not on the circle itself.
Radius: a segment from the center to any point on the circle. All radii of a circle are congruent.
Diameter: a chord passing through the center. $d = 2r$.
Chord: a segment with both endpoints on the circle. A diameter is the longest chord.
Secant: a line that intersects the circle at exactly two points (contains a chord).
Tangent: a line that intersects the circle at exactly one point (the point of tangency). A tangent is perpendicular to the radius at the point of tangency.
Arcs
An arc is a connected portion of the circle.
Minor arc: less than a semicircle (arc measure < 180°). Named by two endpoints: $\overset{\frown}{AB}$.
Major arc: more than a semicircle (arc measure > 180°). Named by three points: $\overset{\frown}{ACB}$.
Semicircle: exactly half the circle (arc measure = 180°).
Arc measure: equal to the measure of its central angle.
Central and Inscribed Angles
Central angle: an angle with its vertex at the center of the circle. The central angle intercepts (cuts off) an arc equal to the angle.
$$\text{Arc measure} = \text{central angle measure}$$
Inscribed angle: an angle with its vertex on the circle and sides that are chords. An inscribed angle is half the intercepted arc.
$$\text{Inscribed angle} = \frac{1}{2} \cdot \text{intercepted arc}$$
Example 1 — Naming Arcs
Circle $O$ with points $A$, $B$, $C$ on the circle. Central angle $\angle AOB = 80°$.
Arc $\overset{\frown}{AB} = 80°$ (minor arc)
Major arc $\overset{\frown}{ACB} = 360° - 80° = 280°$ (going around through $C$)