Download Condensed Test

February Regional
Geometry Condensed Team Test
Question #1
A = The value of x if two complementary angles have measures of
and
.
B = The sum, in degrees, of the exterior angles of a nonagon.
C = The sum, in degrees, of the interior angles of a 13 sided polygon.
D = The number of sides of a regular polygon with an interior angle measure of
.
Find the value of 5A-B+2C-2D
Question #2
A = The area of a regular octagon with side length 6.
B = The area of an isosceles trapezoid, with bases of length 8 and 10, and base angle of
.
C = The area of the annulus formed by two concentric circles of radii 15 and 29.
D = The ratio of the perimeter to the area of an equilateral triangle with side length of 13. This ratio
must include a radical.
Find the value of
–
Question # 3
In triangle ABC, side AC=7, side AB=11, and side BC=8.
A = The distance from the incenter of the triangle ABC to side AB.
B = The distance from the circumcenter of triangle ABC to vertex C.
Find the value of
Question #4
Find the length of the longer diagonal of parallelogram ABCD, given that it has an area of 40, side
AD=5, and the sine of the smaller angle of this parallelogram is 4/5.
Question #5
Husayn is on top of a light house when he sees a whale that is 20 m away. If the angle of depression
from Husayn’s eyes to the whale is 60 degree, how far above the ocean are Husayn’s eyes? Assume
that the light house makes a 90 degree angle with the ground.
Question #6
In the figure shown, Segments C and D are parallel, and segments A and B are parallel. Angle 5 is
.
A = The measure of angle 1.
B = The measure of angle 2
C = The measure of angle 3.
D = The measure of angle 4.
Find the value of
Question #7
In the figure shown, points A, B, and C are on circle O. The measure of angle CEA is 2x, the
measure of angle BCA is x, and the measure of angle BAC is 2x.
A = The measure of arc BC in degrees.
B = The measure of arc AB in degrees.
C = The measure of angle ABC in degrees.
Find
Question #8
Triangle ABC has sides of length 6, 10, and some unknown integer.
A=The maximum possible length of the unknown side.
B = The minimum possible length of the unknown side.
C = The number of possible integral lengths for the unknown side.
Find the value of
February Regional
Geometry Condensed Team Test
Question #9
A = The area of a rhombus with one diagonal of length 24, and perimeter of 52.
B = The length of the apothem of a regular hexagon with area
.
C = The area of a circle with semi-circumference
.
D = The shorter height of a parallelogram with area 120, and sides of length 8 and 24.
Find the value of
Question # 10
A = The area of a
sector of a circle with radius 12.
B = The length of a
arc on a circle with diameter 15.
C = The geometric mean of 5, 9, and 25.
D = The number of sides in polygon ABCDEFGHIJKLMNOP.
Find
Question #11
A semicircle with area 8π has a square inscribed in it. Find the ratio of the diagonal of the square to the
perimeter of the semicircle.
Question #12
The sum of the interior angles of a regular polygon in degrees is the equal to 30 times the number of
diagonals, minus the sum of its exterior angles in degrees, minus 15 times the number of vertices it has. What
is the measure of an interior angle of this polygon, in degrees?
Question #13
A large semicircle has a smaller semicircle inscribed in it. This smaller semicircle is inverted. What is the
ratio of the area of the larger semicircle to that of the smaller semicircle?
Question #14
A = The maximum number of regions formed by the intersection of 11 lines.
B = The maximum number of distinct planes that can be formed by 9 points.
C = The maximum number of points of intersection of 7 lines.
D = The number of diagonals of a regular heptagon.
Find
Question #15
In circle C, chord AB has length 10. The radius of circle C drawn to point B makes an angle of
this information, find the area of segment AB of circle C.
. Given