Circles

Radius In a circle, a radius perpendicular to a chord bisects the chord and the arc. In a circle, a radius that bisects a chord is perpendicular to the chord. In a circle, the perpendicular bisector of a chord passes through the center of the circle. If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency. Chords In a circle, or congruent circles, congruent chords are equidistant from the center. (and converse) In a circle, or congruent circles, congruent chords have congruent arcs. (and converse0 In a circle, parallel chords intercept congruent arcs In the same circle, or congruent circles, congruent central angles have congruent chords (and converse) Tangents Tangent segments to a circle from the same external point are congruent Arcs In the same circle, or congruent circles, congruent central angles have congruent arcs. (and converse) Angles An angle inscribed in a semi-circle is a right angle. In a circle, inscribed angles that intercept the same arc are congruent. The opposite angles in a cyclic quadrilateral are supplementary In a circle, or congruent circles, congruent central angles have congruent arcs.