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The following diagrams give a summary of part Chord Theorems: Perpendicular Bisector andCongruent Chords. Scroll down the page for examples, explanations, and 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 to the chord PQ then PA = AQ.
Converse: The perpendicular bisector that a chord passes through the facility of a circle.
In the over circle, OA is the perpendicular bisector that the chord PQ and also it passes with the center of the circle. OB is the perpendicular bisector that the chord RS and it passes with the center of the circle.
We have the right to use this home to discover 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 facility of the one is the allude of intersection of the perpendicular bisectors.
Circles, Radius Chord Relationships, street From The center To A Chord
This video showshow to specify a chord,how to describe the impact of a perpendicular bisector the a chord and the distance from the facility of the circle,that the perpendicular bisector that a chord passes v the center of the circle.
Theorem: Congruent Chords room equidistant native the center of a circle.
Converse: Chords equidistant from the center of a circle are congruent.
If PQ = RS climate OA = OB or If OA = OB then PQ = RS
How To use The Chords Equidistant native The center Of A one Theorem
The to organize states:Chords equidistant from the facility of a circle are congruent.Congruent chords space equidistant native the facility of a circle.
Theorem: If 2 chords in a circle space congruent then your intercepted arcs space congruent.
Converse: If two arcs space congruent climate their equivalent chords are congruent.
Theorem on Chords and Arcs With an example On how To use The Theorem
The following video clip also shows the perpendicular bisector theorem.If a diameter or radius is perpendicular come a chord, climate it bisects the chord and its arc.If two chords are congruent, then their corresponding arcs space congruent.If a diameter or radius is perpendicular come a chord, then it bisects the chord and also its arc.In the same circle or congruent circle, two chords are congruent if and also only if they space equidistant indigenous the center.
Theorem: If 2 chords in a circle space congruent then they identify two main angles that room congruent.
This video discusses the adhering to theorems:Congruent central angles have actually congruent chords,Congruent chords have actually congruent arcs,Congruent arcs have congruent main angles.
This video describes the four properties that chords:If two chords in a circle space congruent, then they identify two main angles that are congruent.If 2 chords in a circle are congruent, then your intercepted arcs are congruent.If two chords in a circle room congruent, then they space equidistant indigenous the center of the circle.The perpendicular native the center of the circle to a chord bisects the chord.
Example: The figure is a circle with center O. Offered PQ = 12 cm. Find the size 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 the a circle if a chord that the circle has a size of 12 cm and also is 4 centimeter from the facility of the circle.
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