Chord Bisector Theorem

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 radius of circle A

•  $\overline{EF}$  is a secant line of circle A

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

•  $\overline{EF}$  is the tangent line of circle A

True or False?
If $\overline{EF}$ is a diameter to Circle A, then  $\overline{BD}\cong\ \overline{DC}$ ,  $\overline{EF}\ \perp\ \overline{BC}$ ,  $measure\ of\ arc\ BE\cong\ measure\ of\ arc\ CE.$  
(Hint: Use Chord Theorem #3)

• True

• False

Determine the value of x and y.

• $x=64^{\circ\ }$ and $y=4$

• $x=4$ and $y=64^{\circ}$

• $x=116^{\circ}$ and $y=4$

• $296^{\circ}$ and $y=4$

Use the diagram of circle A.

Which expression and deductive reasoning can be used to find the value of y?

• $2y+1=\ 5x-18$ 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.

• $y+4=2y+1$ 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.

Determine if the following expression $3x-4=5x-18$  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  $3x-4=5x-18$  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.

  $BD=12$  and  $AC=3$  in circle A. Find the radius  $AB.$  

•  $\sqrt{27}$  

•  $3\sqrt{5}$  

•  $6$  

•  $\sqrt{18}$  

Use the diagram of Circle A for the following question.
If $\overline{BE}\cong\overline{CD}$ , then what can you determine about the arc measures?
(Hint: Use Chord Theorem #1)

•  $measure\ of\ arc\ BE\ +\ measure\ of\ arc\ CD=\ 360^{\circ}$  

•  $measure\ of\ arc\ BE\cong measure\ of\ arc\ CD$  

•  $measure\ of\ arc\ BC\cong measure\ of\ arc\ ED$  

• Not enough information

Use Circle A for the following problem.  
If measure arc BD is  $125^{\circ}$ , then what is the measure of arc CD? 
(Hint: Use Chord Theorem #1)

•  $360^{\circ}$  

•  $140^{\circ}$  

•  $235^{\circ}$  

•  $250^{\circ}$  

Use circle A to answer the following questions. 

If measure of arc BC is  $80^{\circ}$ . Find the measure of arc CD.
Hint: Use the Chord Theorem #1)

•  $140^{\circ}$  

•  $280^{\circ}$  

•  $80^{\circ}$  

•  $250^{\circ}$  

Use circle A to answer the following questions. 

If measure of arc BC is  $80^{\circ}$ . Find the measure of arc CD.
Hint: Use the Chord Theorem #1)

•  $140^{\circ}$  

•  $280^{\circ}$  

•  $80^{\circ}$  

•  $250^{\circ}$