In a circle, if a diameter bisects a chord (that is not a diameter), then:

it is perpendicular to the chord

it is just shaking out the sillies

In a circle, if a diameter is is perpendicular to a chord, then:

it bisects BOTH the chord and its arc

it bisects the corresponding arc

none of these answers are correct

Use the diagram of circle A. Which expression and deductive reasoning can be used to find the value of y?

$$y+4=2y+1$$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chord is divided into two equal halves.

$$2y+1=\ 5x-18$$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chord is equal to its corresponding arc.

$$y+3=3x-4$$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chord is equal to its corresponding arc.

$$y+4+2y+1$$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chords are added together.

Determine if the following expression is true or false. Why?

The expression $$3x-4=5x-18$$ is true because if a diameter is perpendicular to a chord, it is the bisector of the chord and its arcs.

The expression 3x-4=5x-18 3 x − 4 = 5 x − 1 8 is true because if a radius is perpendicular to a chord, it is the bisector of the chord and its arcs.

The expression $$3x-4=5x-18$$ is false because if a diameter is perpendicular to a chord, it is the bisector of the chord only.

The expression $$3x-4=5x-18$$ is false because if a diameter is perpendicular to a tangent line, it is the bisector of the diameter.

Perpendicular Bisector Chord

Authored by Anthony Clark

Mathematics

10th Grade

CCSS covered

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FILL IN THE BLANK QUESTION

1 min • 1 pt

Find the radius of the circle. Round to the nearest tenth.
(Do not include units.)

Tags

CCSS.HSG.C.A.2

FILL IN THE BLANK QUESTION

1 min • 1 pt

Find AC. (Do not include units.)

Tags

CCSS.HSG.C.A.2

FILL IN THE BLANK QUESTION

1 min • 1 pt

Find RS.

Tags

CCSS.HSG.C.A.2

FILL IN THE BLANK QUESTION

1 min • 1 pt

Find RS.
Round to the nearest hundredth.

Tags

CCSS.HSG.C.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

In the given proof, what is the reason for step 1?

Angles that form a linear pair are supplementary.

Angles of Equal Measure are Congruent

Reflexive Property of Congruence

Definition of a Perpendicular Bisector

Tags

CCSS.HSG.SRT.B.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which statement about the perpendicular bisector of this segment is true?

The bisector will intersect at (0,2).

The slope of the bisector is 5/2.

The bisector passes through (-3,2).

The equation of the bisector is y=-2/5x + 2

Tags

CCSS.HSG.GPE.B.6

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Perpendicular Bisector Chord