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Q is the center of both circles and QA=$$\frac{3}{2}$$QX

Quantity A

The length of arc ABC

Quantity B

The length of arc XYZ



Arc AB is on the circle with center O, ∠AOB=90°

Quantity A

The area of the shaded region

Quantity B

The area of the semi-circle OCB with OB as its diameter



In the figure shown above, the area of the shadow is 12π, the small circle is inscribed in the big circle and pass the center of the big circle, what is the diameter of the small circle?
The length of a clock pendulum is 38, when the angle the pendulum goes is x degree, the length of arc it goes is 41, then what is the value of x?
Give your answer to the nearest tenths.

Four identical semi-circles overlap with a square on four sides, respectively. If the sides of the square is 4, and the entire figure is inscribed in a circle. What is the area of the shaded area?


Square ABCD is inscribed in the circle O and AB=2.

Quantity A

The area of ΔAOB

Quantity B

The area of shaded part



Quadrilateral ABCD is a parallelogram, r=2, and ∠DAB=45, what is the area of the shaded region?
In a xy-plane, the center of circle A is in circle B.
Quantity A: The number of intersects of circle A and B
Quantity B:1

As shown in the figure, there are 5 circles inscribed in a rectangle, each circle has a diameter of 4, and the circles are tangent to each other. What is the area of the rectangle?

Five identical small circles are inscribed in a larger circle, and the sum of the diameters of the 5 small circles equal the diameter of the larger circle.

Quantity A

The circumference of the large circle

Quantity B

The sum of the 5 circumferences of the smaller circle



Triangle ABC is inscribed in a circle,where AB is diameter and the length of AC equals to radius R. What is the degree of ∠ABC?
AC is the diameter of a circle, and D is a point on arc ABC of that circle.

Quantity A

∠DCA

Quantity B

45°



Circle A has radius 4.
Circle B has radius 3.

Quantity A

$$x$$

Quantity B

$$y$$



Point A and point B are the centers of two circles, and their radius are 10 and 3 respectively. Point C and point D and the points of tangency of the two circles and a horizontal line. Point E and point F are the intersections between the two circles and line AB, EF=12, what is the length of CD?
The height, width and length ratio of a rectangular solid is 1:2:3, while the surface area of the entire solid is 550. What is the volume of the rectangular solid?
A large cube consists of 216 small identical cubes. What is the number of small cubes that do not have a face that is part of a face of the large cube?


If 20 red cubes and 7 white cubes, all of equal size, are fitted together to form one large cube, as shown above, what is the greatest fraction of the surface area of the large cube that could be red?
The radius of cylinder A is twice as many as the radius of cylinder B, and the height of cylinder A is twice as many as the height of cylinder B, so what is the ratio of the volume of cylinder B to the volume of cylinder A?
Give your answer as a fraction.
Vertical cylinder A and B share the same volume. The base radius of cylinder A is twice as many as that of cylinder B. What is the height ratio of cylinder A and B?
Give your answer as a fraction.
There is a cylindrical swimming pool with a height of 4 feet and a bottom diameter of 10 feet. Now that the water depth is 3 feet and 6 inches, how many gallons of water are in the pool? (π≈3.14,1feet=12 inches,1gallon=243 cubic inches)
Give your answer to the nearest units digit.
_______gallons

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