# Geometry Form A

1. The hypotenuse of a right triangle is

12" long, and one of the acute angles

measures 30 degrees. The length of

the shorter leg must be:

(A) inches (B)
inches

(C) 5 inches (D) 6 inches

(E) 7 inches

2. The sum of the measures of all of the

non-overlapping angles formed by 7

rays drawn on the same side of a line

from the same point of that line is (?)

(A) 1260° (B) 1080° (C) 900°

(D) 360° (E) 180°

3. How many degrees are there in an

angle that measures one-ninth of its

complement?

(A) 810° (B) 162° (C) 81°

(D) 80° (E) 9°

4. Each interior angle of a regular

octagon is:

(A) 120° (B) 144° (C) 135°

(D) 140° (E) 108°

5. ABCD is a rhombus with BC = 5, and

BD = 6. What is the length of CA?

(A) 8 (B) 9 (C) 10

(D) 11 (E) 12

6. Which of the following is true if two

given triangles are not similar?

(A) their areas cannot be equal

(B) they may be congruent

(C) they are not congruent

(D) their corresponding sides may

be proportional

(E) their corresponding angles may be

equal

7. The points (1,2), (- 4,3) and (7,- 6) are

three vertices of a parallelogram. The

fourth vertex is:

(A) (12,- 2) (B) (2,- 11)

(C) (- 11,5) (D) all of these

(E) none of these

8. A triangle and a rectangle have equal

areas. The base and height of the

triangle are 12 and 4, respectively.

Find the width of the rectangle if its

length is 8.

(A) 3 (B) 4 (C) 5

(D) 6 (E) 7

9. A rectangle has length x units and

width y units. The rectangle has the

same perimeter as an equilateral

triangle with a side of m units.

Find x in terms of m and y.

(A) m + y (B) m - y

(C) 3m - 2y

(D) 1/2m + y (E) 1/2(3m - 2y)

10. The side of a cube is decreased by

50%. By how much does the volume

decrease?

(A) 12.5% (B) 25% (C) 50%

(D) 75% (E) 87.5%

11. If the circumference of a circle is 12π

feet, what is the number of square feet

in its area?

(A) 6π (B) 9π (C) 36π

(D) 81π (E) 144π

12. What is the area of a circle inscribed

in a square that has a side length of

8 cm?

(A) 8π cm^{2} (B) 16π cm^{2} (C) 32 π cm^{2}

(D) 64π cm^{2} (E) 48π cm^{2}

13. In circle C, minor arc XK is 1 / 3 of the

circumference of the circle. If F is not

on minor arc XK, what is the measure

of inscribed angle XFK ?

(A) 60° (B) 30° (C) 15°

(D) 120° (E) 300°

14. Find the area of the shaded part of the

figure:

(A) 25cm^{2} (B) 50cm^{2} (C) 35cm^{2}

(D) 37.5 cm^{2} (E) 12.5 cm^{2}

15. If a quadrilateral is inscribed in a

circle, the opposite angles are:

(A) congruent (B) obtuse

(C) complementary (D) acute

(E) supplementary

16. A circle can be inscribed in:

(A) any triangle (B) any octagon

(C) any trapezoid (D) any polygon

(E) any parallelogram

17. The area of a trapezoid is 160 square

units, one base is 26 units, and the

height is 8 units. What is the length of

the other base?

(A) 7 (B) 14 (C) 56

(D) 6 (E) 80 / 17

18. A square piece of paper, with one side

equal to 12 units, is folded so that the

four corners of the square meet in the

center of the square. This forms a new

square. What is the side measure of

the new square?

(A) 5 (B) (C)

(D) 6 (E) 8

19. The diameter of the front wheel of a

tricycle is 8" and the diameter of each

rear wheel is 3". How many

revolutions has each back wheel

made while the front wheel has

turned 1440 degrees?

(A)

(B) 4 (C)

(D) 24 (E) 96

20. A circular track has a radius of 210

feet. Approximately how many times

must a jogger circle the track in order

to jog one mile?

(A) 20 (B) 4 (C) 35

(D) 39 (E) 34

21. The value of B is:

(A) 3.14 (B) 3.1415

(C) 3.141592 (D) 3.1415926535

(E) none of these

22. The area of a circle inscribed in an

equilateral triangle is 4p. What is the

height of the triangle?

(A) 2 (B) 4 (C) 6

(D) 8 (E) 10

23. The sum of the exterior angles of any

polygon will always be what measure?

(A) 180°

(B) 360°

(C) (n – 2) 180°

(D) (n + 2) 180°

(E) none of these

24. The area of a square 18 ft. on a side

is equal to the area of a rectangle

with a length of 3 yards. The width of

this rectangle is:

(A) 2 ft. (B) 9 ft. (C) 18 ft.

(D) 36 ft. (E) 27 ft.

25. The set of points in a plane at a fixed

distance from a given point in that

plane is:

(A) a line (B) a circle (C) an angle

(D) two lines (E) a point

26. The radii of two circles are 3 cm and

5 cm, respectively. Find the radius of

the circle whose area is equal to the

sum of the areas of the two given

circles.

(A) 8 (B) 34 (C)

(D) 34π (E) none of these

27. Three lines lie in one plane. Line m

intersects line n which is parallel to

line p. How many points are

equidistant from all three lines at the

same time?

(A) 2 (B) 1 (C) 0

(D) 4 (E) 8

28. A sector of a circle has the same area

as an equilateral triangle whose base

is 12. What is the area of the sector?

(A) (B)
(C) 12

(D) 144 (E) none of these

29. The number of points on a circle that

are equidistant from the endpoints of a

given diameter is:

(A) 1 (B) 2 (C) 3

(D) 4 (E) 5

30. The radius of a circle is increased by

50%. By how much does the area

increase?

(A) 25% (B) 50% (C) 100%

(D) 125% (E) 250%

31. In the figure, AB = AC, DB = DC,

πABC = ½ πDBC, and pD = 70°.

How many degrees are there in πA?

(A) 55 (B) 70 (C) 105

(D) 110 (E) 125

32. QRST is a quadrilateral with TQ ┴ TS

and QR ┴ RS as shown in the figure

below. If QT = 70m, SR = 200m, and

TS = 240 m, how many square

meters are there in quadrilateral

QRST?

(A) 2340 (B) 16800 (C) 22400

(D) 23400 (E) 46800

33. Given line QT which goes through the

center of a circle with center C, whose

radius is 4 and P lies on the circle.

If PT = 4 and CQ =4 find the measure

of the angle x = πPQC.

(A) x < 20° (B) 20° # x < 30°

(C) 30° # x < 40° (D) 40° # x < 50°

(E)

34. Two sides of a triangle are 12 cm and

8 cm, respectively. The altitude to the

12 cm side is 4 cm. Find the altitude to

the 8 cm side.

(A) 3 cm (B) 24 cm (C) 12 cm

(D) 6 cm (E) 8 / 3 cm

35. Given quadrilateral PQRS inscribed in

a circle with side PQ extended

beyond Q to point T. How many

degrees are in πTQR if πQPS = 110

degrees, & πPSR = 40 degrees?

(A) 30 (B) 70 (C) 140

(D) 40 (E) 110

36. In the figure below, AB ┴ BC,

BC ┴ CD, AB = 8, BC = 5, CD = 4.

What is the shortest distance from

A to D?

(A) 12 (B) 13 (C) 15

(D) 16 (E) 17

37. What is the effect on the volume of a

cylinder if the diameter is doubled

and the height is cut in half?

(A) the volume remains the same

(B) the volume is doubled

(C) the volume is cut in half

(D) the volume increases by a

factor of four

(E) none of these

38. What is the length of AF in this cube

that has edges 1 cm long?

(D) 1 (E) none of these

39. A point P is selected at random on a

semicircle with diameter RS. T is the

foot of the perpendicular from P to RS.

If RS = 6 and RT = x, then the length

of PT in terms of x is:

40. In the figure below, the large circle

has diameter AC. The two small

circles have their centers on AC and

are tangent to each other at the center

of the large circle. Find the area of the

shaded region, given that AC = 4.

(A) 16π (B) 4π (C) 2π

(D) 1π (E) none of these