1. Tad constructs two circles that are tangent to one another. Which of the following statements is always true concerning these circles?

[1] One circle is in the interior of the other circle.

[2] The two circles are congruent.

[3] The two circles are similar.

[4] The two circles have equal area.

2. ΔABC is an isosceles triangle with . If m ∠A = 3x + 6 and m ∠B = 6x , find m ∠C .
[1] 14º

[2] 48º

[3] 70º

[4] 84º

3. Lines m and n are parallel with m ∠2 = x ² - 10x and
m ∠1 = 2x + 132. What is the m ∠3?

[1] 12º

[2] 24º

[3] 30º

[4] 40º

4. A circle with a center at (2,1) passes through the point (5,4). What is the length of the diameter of this circle?

5. Point P is a point located on segment such that AP:PB =1:2. If A (-4,-5) and P (-2,-1), find the coordinates of point B .

6. What is the smallest number of degrees by which a regular hexagon may be rotated about its center and appear unchanged?

7. Which of the following statements will prove that a quadrilateral is a rhombus?

[1] The opposite sides are parallel and congruent.

[2] The diagonals are congruent and perpendicular.

[3] Both pairs of opposite sides are congruent and the adjacent sides are perpendicular.

[4] The diagonals are perpendicular and bisect each other.

8. What is the center, C , and the radius, r , of a circle with the equation x ^{2} - 4x + y ^{2} + 6y = 3 ?

9. Which transformation on ΔABC will result in image ΔA'B'C' , as shown on the graph at the right?

10. Tanya is attempting to inscribe a circle in a triangle by construction.
Which construction must she use to locate the center of the circle?

11.

12. As seen at the right, and BE = 8.
If CD : DA = 2 : 5,
what is AB ?

13. In ΔRST, m ∠R = 35º and m ∠S = 65º. Which choice is accurate as to the lengths of the sides of the triangle?

14 . Given that sin(2x + 10) = cos(3x + 40), find the number of degrees in the acute angles of the corresponding right triangle.

[1] 20º and 70º

[2] 25º and 65º

[3] 26º and 64º

[4] 30º and 60º

15. A roof is modeled by ΔPQR where and
. If m ∠QPS = 28º and PR = 28 feet, what is QS , to the nearest tenth of a foot ?

16. A quadrilateral, PQRS , is inscribed in a circle. Which statement is true about this diagram?

17. Which linear equation is not parallel to the other linear equations listed?

18. In isosceles ΔABC , and median is drawn. Prior to proving that is also an altitude, it will be necessary to prove by _____.

19. A cylinder has a radius of 6 and a height of 12. A cone has the same radius, but need to have the same volume as the cylinder. What must be the height of the cone so its volume will be the same as the volume of the cylinder?

[1] 6

[2] 12

[3] 24

[4] 36

20. In circle O,

AP =

,

PB =

x and

BC = 3.

Find the value of

x .

21. Which of the following triangles are always similar?

22. In the diagram at the right, , and .
What is the value of x ?

23. In circle O , the arcs are in the ratio EF:FG:GH:HE = 2 : 5 : 4 : 7.
What is the m ∠EMF ?

24. What is the radian measure of the smaller angle formed by the hands of a clock at 4 pm?.