If $$\overline{BD}\cong\overline{DC}$$ and $$\overline{EF}\ \perp\ \overline{BC}$$ , what conclusions can say about $$\overline{EF}$$ ? (Hint: Use Chord Theorem #2)

$$\overline{EF}$$ is the diameter of circle A

\overline{EF} E F is the radius of circle A

\overline{EF} E F is a secant line of circle A

\overline{EF} E F is the tangent line of circle A

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.

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

Apply Properties of Chords

Authored by Anthony Clark

Mathematics

10th Grade

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$\overline{EF}$

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Apply Properties of Chords

Use the following diagram. What is the value of x and y?

Determine the value of x and y.

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

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