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题目内容


Triangle ABC is inscribed in the circle.

Quantity A

The radius of the circle

Quantity B

The length of AC




Quantity A

$$\frac{y}{x}$$

Quantity B

$$\frac{x+y}{2}$$




In the circle shown above, the radius is 4. ABC is an isosceles triangle, CD is perpendicular to AB, what is the length of AB?
Circle X and circle Y have the same area. The radius of circle A is twice the radius of circle X. The diameter of circle B is 75 percent greater than the diameter of circle Y.

Quantity A

The area of circle A

Quantity B

The area of circle B


In the ceiling of a room, an opening was cut in the shape of a square with sides that are 1 foot in length. A circular fixture will be placed over the opening. If the circular fixture covers the square opening completely, which of the following could be the diameter of the circular fixture, in inches? (Note: 1 foot = 12 inches)

Indicate all such diameters.
A square is inscribed in a circle which has a radius of 3

Quantity A

The area of the square

Quantity B

20


Between two concentric circles, one with radius r and another with radius (r+2)

Quantity A

The area of the smaller circle with radius r

Quantity B

The area of the region between these two concentric circles




The center of each of the five circles is point O. The radii of the five circles, from smallest to largest, are $$r$$, $$2r$$, $$3r$$, $$4r$$, and $$5r$$, respectively.

Quantity A

The area of the shaded region

Quantity B

The area of the striped region




The centers of the five smaller circles all lie on segment AB, which is a diameter of the largest circle, and each circle is tangent to two of the other circles.

Quantity A

The circumference of the largest circle

Quantity B

The sum of the circumferences of the five smaller circles




两个转轮绕一个传送带,转轮半径4,顺时针转速26圈/分钟,传送带从A到B传送距离2600,问一个物品放在左边转轮圆心正上方,传送到右边转轮圆心正上方,需要花多长时间?
A bicycle is traveling at a constant rate such that the wheels rotate 72 degrees per 0.1 second. If each wheel of the bicycle has a diameter of 26 inches, how many inches does the bicycle travel in 2 seconds?
The circumference of a certain circular region is y.

Quantity A

The area of the circular region

Quantity B

$$\frac{y^{2}}{4}$$




The figure shows a window that is in the shape of a rectangle with a semicircle at the top. The radius of the semicircle is x feet, and the perimeter of the window is 26 feet. What is the total area, in square feet, of the window in terms of x?


A certain closed curve consists of n semicircles having the same radius of $$\frac{r}{n}$$ together with a larger semicircle having a radius of r. The n semicircles are aligned along the diameter of the larger semicircle as indicated in the figure for n=7. The area of the region enclosed by the curve, in terms of n, and r, is which of the following?


The area of the shaded semicircular region is 64π.

Quantity A

The length of radius OR

Quantity B

10




In the figure above. O is the center of the circle. If minor arc AB has length 2π, what is the area of triangular region AOB?


The outline of a tyre can be roughly seen as two concentric circles. The radius of the larger circle is 8, while the radius of the smaller circle is 6. If the tyre revolve clockwise so that point y on the larger circle travels by d, then how long will a point x on the smaller circle travel?


The figure shows square ABCD inscribed in a circle. What is the ratio of arc ABC to the sum of lengths of line segments AB, BD and CD?


A pendulum 36 inches long swings through an angle of x degrees, and its pointed end travels through a distance of 41 inches before swinging back again, as shown in the figure. Which of the following is closest to the value of x?


In the above two concentric circles, the radius of the outside circle is twice as many as that of the inner one. Line segment BC is tangent to the inner circle. What is the central angle corresponding to arc ACB?

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