You are watching: What do you know about chords that are equidistant from the center of the circle?

The following diagrams offer a review of part Chord Theorems: Perpendicular Bisector andCongruent Chords. Scroll under the web page for examples, explanations, and also solutions.

A **chord** is a right line joining 2 point out on thecircumference the a circle.

**Theorem: A radius or diameter that is perpendicular to a chord divides the chord right into two same parts and vice versa.**

In the over circle, if the radius OB is perpendicular come the chord PQ climate PA = AQ.

Converse: The perpendicular bisector that a chord passes v the center of a circle.

In the above circle, OA is the perpendicular bisector the the chord PQ and it passes through the center of the circle. OB is the perpendicular bisector of the chord RS and it passes v the facility of the circle.

We have the right to use this home to discover the center of any kind of given circle.

Example:Determine the center of the following circle.

Solution:Step 1: draw 2 non-parallel chords

Step 2: construct perpendicular bisectors for both the chords. The center of the one is the suggest of intersection of the perpendicular bisectors.

### Circles, Radius Chord Relationships, street From The center To A Chord

This video clip shows

how to define a chord,how to explain the result of a perpendicular bisector of a chord and the distance from the center of the circle,that the perpendicular bisector the a chord passes through the center of the circle.Theorem: Congruent Chords room equidistant native the facility of a circle.

Converse: Chords equidistant indigenous the facility of a circle room congruent.

If *PQ* = *RS* then *OA* = *OB* or If *OA* = *OB* then *PQ* = *RS*

### How To usage The Chords Equidistant native The center Of A circle Theorem

The theorem states:

Chords equidistant from the center of a circle room congruent.Congruent chords space equidistant indigenous the center of a circle.Theorem: If 2 chords in a circle space congruent then their intercepted arcs space congruent.

Converse: If two arcs room congruent climate their equivalent chords space congruent.

### Theorem on Chords and Arcs With an example On how To usage The Theorem

The following video clip also shows the perpendicular bisector theorem.

If a diameter or radius is perpendicular to a chord, climate it bisects the chord and also its arc.If two chords are congruent, then their matching arcs space congruent.If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.In the very same circle or congruent circle, 2 chords space congruent if and also only if they space equidistant native the center.Theorem: If 2 chords in a circle room congruent climate they identify two main angles that room congruent.

This video clip discusses the following theorems:

Congruent main angles have congruent chords,Congruent chords have congruent arcs,Congruent arcs have actually congruent main angles.This video describes the four properties of chords:

If 2 chords in a circle space congruent, then they recognize two central angles that space congruent.If two chords in a circle room congruent, then your intercepted arcs room congruent.If two chords in a circle are congruent, climate they are equidistant native the facility of the circle.The perpendicular native the center of the circle come a chord bisects the chord.Example: The number is a one with facility O. Given PQ = 12 cm. Uncover the length of PA.

Example: The number is a circle with facility O and also diameter 10 cm. PQ = 1 cm. Discover the size of RS.

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Example:Find the length of the radius that a circle if a chord of the circle has a size of 12 cm and also is 4 centimeter from the center of the circle.

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