Geometry Theorems 12-4 through 12-10

Theorem 12-9

In a circle, if a diameter bisects a chord (that is not a diameter), then it is perpendicular to the chord.

Theorem 12-8

Theorem In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.

Theorem 12-10

Theorem In a circle, the perpendicular bisector of a chord contains the center of the circle.

Theorem 12-7 and its converse

Theorem Within a circle or in congruent circles, chords equildistant from the center or centers are congruent. Converse Within a circle or within congruent circles, congruent chords are equildistant from the center or centers.

Theorem 12-5 and its converse

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

Theorem 12-6 and its converse

Theorem Within a circle or in congruent circles, congruent chords have congruent arcs. Converse Within a circle or in congruent circles, congruent arcs have congruent chords.

Theorem 12-4 and its converse

Theorems Within a circle or in congruent circles, congruent central angles have congruent arcs Converse Within a circle or in congruent circles, congruent arcs have congruent central angles