Perpendicular bisector the a chord passes through the center of a circle.Congruent chords are equidistant native the facility of a circle.If two chords in a circle room congruent, then your intercepted arcs are congruent.If two chords in a circle space congruent, then they identify two central angles that are congruent.

You are watching: If two chords of a given circle are congruent then they must

The complying with diagrams give a summary of some Chord Theorems: Perpendicular Bisector andCongruent Chords. Scroll under the web page for examples, explanations, and also solutions.

A chord is a right line authorized 2 points on thecircumference of a circle.

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

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

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

In the over circle, OA is the perpendicular bisector of the chord PQ and it passes with the center of the circle. OB is the perpendicular bisector that the chord RS and also it passes v the center of the circle.

We deserve to use this home to find the center of any given circle.

Example:Determine the center of the adhering to circle.

Solution:Step 1: attract 2 non-parallel chords

Step 2: construct perpendicular bisectors because that both the chords. The center of the circle is the suggest of intersection of the perpendicular bisectors.

Circles, Radius Chord Relationships, distance From The facility To A Chord

This video clip shows

how to specify a chord,how to describe the impact of a perpendicular bisector that a chord and also the distance from the center of the circle,that the perpendicular bisector that a chord passes with the center of the circle.

Theorem: Congruent Chords space equidistant native the center of a circle.

Converse: Chords equidistant from the facility of a circle space congruent.

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

How To usage The Chords Equidistant indigenous The facility Of A circle Theorem

The to organize states:

Chords equidistant from the facility of a circle are congruent.Congruent chords space equidistant indigenous the facility of a circle.

Theorem: If 2 chords in a circle room congruent then your intercepted arcs space congruent.

Converse: If 2 arcs space congruent then their corresponding chords space congruent.

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

The following video clip also mirrors the perpendicular bisector theorem.

If a diameter or radius is perpendicular to a chord, climate it bisects the chord and its arc.If 2 chords space congruent, then their corresponding arcs space congruent.If a diameter or radius is perpendicular to a chord, then it bisects the chord and also its arc.In the exact same circle or congruent circle, two chords are congruent if and also only if they space equidistant native the center.

Theorem: If 2 chords in a circle room congruent then they recognize two central angles that space congruent.

This video discusses the adhering to theorems:

Congruent central 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 two chords in a circle are congruent, climate they recognize two main angles that are congruent.If two chords in a circle space congruent, then their intercepted arcs room congruent.If 2 chords in a circle space congruent, then they space equidistant native the center of the circle.The perpendicular indigenous the facility of the circle to a chord bisects the chord.

Example: The figure is a one with center 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. Uncover the length of RS.

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

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