Geometry

Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π 100 π 100 square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains ? (1) Jack's rug covers an area of 9π square feet. (2) The centers of the stains are less than 4 feet apart.

What is the circumference of circle C ? (1) The radius of circle C is 2π. (2) The center of circle C is located at point (7,8) in the xy-plane.

In the xy-coordinate plane, what are the x-coordinates of the four vertices of square JKMN ? (1) J and M are on the x-axis, and K and N are on the y-axis. (2) The center of the square is at the origin.

The figure above represents an L-shaped garden. What is the value of k? (1) The area of the garden is 189 square feet. (2) The perimeter of the garden is 60 feet.

In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle? (1) AB = 3 and BC = 2 (2) CD = 1 and DE = 4

In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ? (1) s = 40 (2) r = 70

In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel? (1) The maximum width of the truck is 2.4 m (2) The maximum height of the truck is 4 m

Square ABCD is inscribed in circle O. What is the area of square region ABCD? (1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.

What is the number of cans that can be packed in a certain carton? (1) The interior volume of this carton is 2,304 cubic inches. (2) The exterior of each can is 6 inches high and has a diameter of 4 inches.

A pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. Is the perimeter of the pentagon greater than 26 centimeters? (1) The area of the circle is 16π square centimeters. (2) The length of each diagonal of the pentagon is less than 8 centimeters.

In the figure above, is the area of triangular region ABC equal to the area of triangular region DBA ? (1) (AC)^2=2(AD)^2 (2) ∆ABC is isosceles. Source: OG13

A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank? (1) The inside of the tank is exactly 4 feet in diameter. (2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet. From OG 2016 (question 86 DS)

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle? (1) The area of the triangle is 25 square centimeters. (2) The 2 legs of the triangle are of equal length.

In the figure above, if A, B, and C are the areas, respectively, of the three nonoverlapping regions formed by the intersection of two circles of equal area, what is the value of B + C ? (1) A + 2B + C = 24 (2) A + C = 18 and B = 3

Is the point Q on the circle with center C ? (1) R is a point on the circle and the distance from Q to R is equal to the distance from Q to C. (2) S is a point on the circle and the distance from Q to S is equal to the distance from S to C.

Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length.

In the figure above, if the area of triangular region D is 4, what is the length of a side of square region A ? (1) The area of square region B is 9. (2) The area of square region C is 64/9.

In the figure above, ΔPQR has angle measures as shown. Is x < y ? (1) PQ = QR (2) PR > QR

If all of the six faces of a concrete block are rectangular, what is the volume of the block? (1) Each of the four lateral faces of the block has an area of 200 square inches. (2) The top of the block is square and has an area of 400 square inches.

The figure above represents a box that has the shape of a cube. What is the volume of the box? (1) PR = 10 cm (2) Q T = 5 6 √ Q T = 5 6 cm