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Circle Theorem: Arcs and Chords

High School Math based on the topics required for the Regents Exam conducted by NYSED.

Theorems:

In a circle, or congruent circles, congruent chords are equidistant from the center. (converse) In a circle, or congruent circles, chords equidistant from the center are congruent.

In a circle, or congruent circles, congruent chords have congruent arcs.
(converse) In a circle, or congruent circles, congruent arcs have congruent chords.

In a circle, a radius perpendicular to a chord bisects the chord.
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.

Arcs and Chords
This video will demonstrate three theorems relevant to arcs and chords as well as outline of the proofs for these theorems. Congruent chords create congruent arcs. Congruent chords are equidistant to the center. If a diameter is perpendicular to a chord then the chord and arc are bisected.

Circle Chord :
A chord is a line segment whose endpoints are on a circle. If a chord passes through the center of the circle, it is called a diameter. Two important facts about a circle chord are that (1) the perpendicular bisector of any chord passes through the center of a circle and (2) congruent chords are the same distance (equidistant) from the center of the circle.

Circle Geometry:
Using Chords Equidistant From the Center This geometry video math lesson deals with circle geometry. The main focus of this video is using the Chords Equidistant from the Center of a Circle Theorem. The theorem states: chords equidistant from the center of a circle are congruent and congruent chords are equidistant from the center of a circle.

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