Math Challenge #22: What is the length of DC

GRE Math Challenge Question #22:

Point O is the center of the circle.

If the area of the circle is 36p and the area of the rectangle is 72, what is the length of DC?

A. 5
B. 6
C. 7
D. 8
E. None of the choices

Solution and Explanation:

Correct Choice : B ( 6 )

The area of this circle is 36π and the area of any circle is πr^2, so the radius of this circle is 6. Label both radius (OA and OD) as 6. Because ABCO is a rectangle, its area is base times height, where radius OA is the height.

Area of a rectangle = bh
72 = b(6)
b = 12

Since OC is a base of the rectangle, it is equal to 12.

Subtract radius OD from base OC to get the length of segment

DC: 12 - 6 = 6.


Click For More Challenge Questions