Practice Page
Directions: Read each question carefully. Choose the best answer.
1.
In the diagram of a construction at the right,
a) what is the measure of ∠AOB?
Choose:
30º
 45º 60º 80º

b) what is the measure of ∠BCD?
Choose:
60º
 120º 135º 160º

 

 

2.
In the construction of a square inscribed in a circle, which step follows drawing the circle?

Choose:
draw the square
bisect the diameter
draw a diameter
construct ⊥ at the center

 

 

3.
The diagram at the right shows the construction of a regular hexagon inscribed in a circle. Two additional segments have been added (red).
What type of triangle is ΔPBC ?
Choose:
acute triangle
equilateral triangle
right triangle
obtuse triangle

 

 

4.
A square is inscribed in a circle, as shown, using only the construction "perpendicular at a point on a line", with the point being the circle's center and the line being the diameter.

Normally, this construction uses a "perpendicular bisector" of the diameter, thus doing both "perpendicularity" and "bisection".
Why is this method also acceptable?
 
Choose:
The "perpendicular at a point on a line" construction automatically bisects the line it intersects.
The center of the circle is already the bisector of the diameter, so you only need the ⊥ portion.
The perpendicular is vertical therefore it bisects the diameter.
This is not an acceptable method for this construction.

 

 

5.
The construction shown below starts with circle O. Circles Q and P each have the same radius as circle O, and pass through point O.
 

a) What is the measure of ∠OAP ?
Choose:
30º
 45º
60º
80º

b) Which of the following statements is NOT true regarding this construction as shown?
Choose:
ΔQBO is an equilateral triangle.
The distance from point A to point B equals the radius length.
The horizontal length of the construction is equal to the length of three diameters.
The figure QBAP is an isosceles trapezoid.

c) This technique is a sufficient method for constructing a regular hexagon inscribed in a circle, with the stipulation that ...
Choose:
the centers of the three circles lie on the same straight line.
the length of the radii must be greater than 1 inch.
the ratio of the height of the construction to its width be 2 to 3.
the distance from point A to point B is greater than the radius.

 

 

6.
When constructing a tangent to a circle at a point ON the circle, which construction is used?

Choose:
Construct a perpendicular bisector of the diameter of the circle.
Construct a perpendicular to the center point of the circle.
Construct a perpendicular at the point where any line intersects with the circle.
Construct a perpendicular to the point where an extended radius of the circle intersects with the circle.

 

 

7.
You are given the task of finding the center of a circle in which the center in not indicated. The theorem "In a circle, the perpendicular bisector of a chord passes through the center of the circle." is used for this construction. Which of the following choices will not be an option for this construction?

Choose:
Construct the perpendicular bisector of two parallel chords.
Construct the perpendicular bisector of the sides of an inscribed angle.
Construct the perpendicular bisectors of two intersecting chords.
Construct the perpendicular bisectors of two sides of an inscribed quadrilateral..

 

 

8.
In the construction shown at the right, a) what is the measure of ∠ADB?
Choose:
15º
 30º 45º 60º

b) What is the measure of ∠ABC?
Choose:
60º
 75º 80º 90º

c) What is the measure of the arc intercepted by two adjacent sides of the square?
Choose:
60º
 90º 180º 270º

 

 

9.
Regarding the construction shown at the right, what is the measure of ∠AOC?

Choose:
100º
120º
130º
160º


 

10.
When inscribing a square in a circle, using the method shown at the right, you are relying on which fact about squares?

Choose:
They contain four right angles.
They have opposite angles congruent.
The diagonals are congruent and perpsymbol.
The diagonals bisect the angles.
squaresmall

 

 

11.
When preparing the construction of a regular hexagon inscribed in a circle, which of the following statements is NOT true?

Choose:
The length of the radius of the circle becomes the length of each side of the hexagon.
The interior angles of the hexagon each contain 60º.
A series of 6 congruent equilateral triangles can be formed in the interior of the hexagon.
The perimeter of the hexagon is equal in length to the length of three diameters of the circle.

 

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