Download Test - FloridaMAO

February Regional
Geometry Individual
For all questions, NOTA is defined as “None of the above answers is correct”.
1) In right triangle ABC, with hypotenuse BC, side AB has length 36, and side AC has length 72.
Find the length of the altitude from vertex A to the hypotenuse.
A.
B.
C.
D.
E. NOTA
2) What is the square root of the arithmetic mean of 7 and the geometric mean of 11 and 1331?
A. 11
B.
C. 12
D. 8
E. NOTA
3) A given triangle has 2 sides of length 5 and 12. How many possible integral lengths are there for
the remaining side?
A. 11
B. 9
C. 10
D. 8
4) Find the supplement of the complement of the complement of an angle of
A.
B.
C.
D.
E. NOTA
.
E. NOTA
5) An equilateral triangle of side length 8 has a circle circumscribed about it. What is the area inside
the circle, but outside the triangle?
A.
B.
C.
D.
E. NOTA
6) The angles of a triangle are 2x, 7x – 15, and 6x. What is the complement of the largest angle in
this triangle?
A. 14
B. 12
C. 15
D. 13
7) In the following figure, segment AE is tangent to circle D at
point A, and segment EC intersects circle D at points B and C.
Given that segment AE=9, and the radius of circle D is 6, find
the length of segment CE.
A.
D. 63/12
B.
E. NOTA
C. 12
E. NOTA
February Regional
Geometry Individual
8) How many diagonals are there in a convex undecagon?
A. 44
B. 14
C. 65
D. 27
E. NOTA
9) In a right triangle with sides of lengths 6, 8, and 10, what is the sum of the squares of the lengths
of the medians?
A. 140
B. 150
C. 130
D. 120
E. NOTA
10) On a hot day, at 12:00 PM, a 10 meter tall tree makes a shadow of length 3 m. At the same time,
Gulete, who is 2 m tall, is standing adjacent to the tree. What is the length, in meters, of Gulete’s
shadow?
A. 6/7
B. 7/6
C. 2/3
D. 3/5
E. NOTA
11) In an isosceles trapezoid with bases of length 10 and 6, one of the legs has length
the area of this trapezoid?
. What is
A.
E. NOTA
B.
C. 16
D. 32
12) Triangle A has angles 6x, -x +30, and y. Pentagon B has angles 7y, -4y-1, x-y, 6x, and 81+7x.
Find the value of x + y.
A. 82/3
B. 41/2
C. 41
D. -10
E. NOTA
13) In a kite, the diagonals have lengths of 121 and 16. Find the area of the kite.
A. 1768
B. 968
C. 1936
D. 884
E. NOTA
14) Which of the following is not a property of rhombi?
A. opposite angles are congruent
B. diagonals bisect each other
C. adjacent angles are supplementary D. opposite sides are congruent
15) Two vertical angles have measures of
A.
B. 252/5
E. NOTA
. Find the value of x.
C. 152/6
D. 302/6
E. NOTA
February Regional
Geometry Individual
16) In the diagram to the right, segment BC is parallel to segment
ED. segment AB=5, segment BC=12, BE=x, and ED=3x+1. Find the
length of segment AE.
A.
B. 70/3
C. 55/3
D. 56
E. NOTA
17) A rhombus has diagonals of lengths 36 and 24. Find the perimeter of the rhombus.
A.
B. 150
C. 432
D.
E. NOTA
18) The area of a square is doubled. What is the ratio of the perimeter of the larger square to that of
the smaller square?
A.
B.
C.
D. 2
E. NOTA
19) Which of the following is defined as the intersection of the altitudes of a scalene triangle.
A. Incenter
B. Orthocenter
C. Centroid
20) A regular polygon has an interior angle with measure
have?
A. 40
B. 30
C. 10
21) What is
D. Circumcenter
E. NOTA
. How many sides does this polygon
D. 20
E. NOTA
D. 1
E. NOTA
equal to?
A. Not enough information
B.
C.
22) Husayn wants to build a rectangular fence. In order to conserve the 6 units of fencing he has, he
decides to use a wall of his house as one of the sides. What is the maximum possible area of this
fence?
A. 9/2
B. 4
C. 8
D. 9
E. NOTA
23) In a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into segments of
length 5 and 45. What is the length of this altitude?
A. 12
B. 9
C.
D. 15
E. NOTA
February Regional
Geometry Individual
24) Two parallel lines are cut by a transversal. How many of the following statements are true?
I.
II.
III.
IV.
Consecutive angles are supplementary.
Same side exterior angles are congruent.
Alternate interior angles are supplementary.
Vertical angles are congruent.
A.
B. 0
C. 2
D.1
E. NOTA
D.
E. NOTA
25) What is the distance between the points (2, 4) and (4, 6)?
A.
B.
C.
26) Given that
is a true statement, which of the following statements must be true?
A.
B.
C.
D.
E. NOTA
27) At the end of a business conference, all of the 13 attendees shake hands with each other 1 time.
How many handshakes occur?
A. 78
B. 64
C. 58
D. 84
E. NOTA
28) In circle O, two chords, AB and CD, intersect at point E. If AE is of length 5, ED is of length 10,
and EB is 15 less than the square of CE, then what is the geometric mean of the lengths of the chords
AB and CD?
A.
B. 5
C. 15
29) A sector of a circle has angle measure of
that the radius of the circle is 6?
A.
B.
D. 50
E. NOTA
degrees. What is the area of this sector, given
C.
D.
E. NOTA
30) An analog clock shows that the time is exactly 7:36. What is the angle, in degrees, between the
hour and minute hands of the clock?
A.
B.
C.
D.
E. NOTA