U10L1 Parts of a Circle

Vocabulary flashcards covering the fundamental parts and relationships of circles, tangents, and intersecting circles.

Circle

The set of all points in a plane that are equidistant from a single point called the center.

Center (of a circle)

The fixed point from which every point on the circle is the same distance.

Radius

A segment that connects the center of the circle to any point on the circle.

Chord

A segment whose endpoints both lie on the circle.

Diameter

A chord that passes through the center of the circle; it is twice the length of the radius.

Secant

A line that intersects a circle at exactly two points.

Tangent (line)

A line that intersects a circle at exactly one point, called the point of tangency.

Point of Tangency

The specific point at which a tangent line touches the circle.

Tangent Circles

Two coplanar circles that intersect in exactly one point.

Externally Tangent Circles

Tangent circles whose centers lie on opposite sides of the common tangent line; the circles touch from the outside.

Internally Tangent Circles

Tangent circles where one circle lies inside the other and they touch at exactly one point.

Concentric Circles

Coplanar circles that share the same center but have different radii.

Common Tangent

A line or segment that is tangent to two coplanar circles.

Common External Tangent

A common tangent that does NOT intersect the segment joining the centers of the two circles.

Common Internal Tangent

A common tangent that DOES intersect the segment joining the centers of the two circles.

Tangent Theorem

A line is tangent to a circle if and only if it is perpendicular to the radius drawn to the point of tangency.

Tangent Segment Theorem

If two segments from the same exterior point are tangent to a circle, then they are congruent.

Radius-Chord Theorem

If a radius is perpendicular to a chord, then the radius bisects the chord and its arc.

Diameter-Chord Theorem

If one chord is the perpendicular bisector of another chord, then the first chord is a diameter.

Chord Theorems

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Chord Congruency Theorem

In the same circle or in two congruent circles, two chords are congruent if and only if they are equidistant from the center.