Circle Theorems

Flashcards covering key theorems related to circles, tangents, chords, and arcs.

Tangent Line Theorem

If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.

Tangent Line Converse Theorem

If a line in the plane of a circle is perpendicular to the radius at its endpoint on the circle, then the line is tangent to the circle.

Two Tangent Segments Theorem

If two tangent segments share a common endpoint, then the segments are congruent.

Congruent Central Angles Theorem

Within a circle or congruent circles, congruent central angles have congruent intercepted arcs.

Congruent Central Angles and Chords Theorem

Within a circle or congruent circles, congruent central angles have congruent chords.

Congruent Chords and Arcs Theorem

Within a circle or congruent circles, congruent chords have congruent arcs.

Chords Equidistant from Center Theorem

Chords equidistant from the center of a circle are congruent.

Diameter Perpendicular to Chord Theorem

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

Perpendicular Bisector of Chord Theorem

The perpendicular bisector of a chord contains the center of the circle.