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If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?
A. 5/8
B. 2/3
C. 11/16
D. 3/4
E. 7/9
The OA is D.
I get the solution to this PS question as follow,
Radius of smaller circle = r2.
Radius of bigger circle = r1.
r1 = 2r2.
Portion of the area of the shaded region: pir2^2.
pi(2r2)^2 - pi r2^2 = 3/4 pi r1^2.
What portion of the area of the larger circle is shaded?
(3/4 pi r1^2)/(pi r1^2) = 3/4. Option C.
Experts, any suggestion? Thanks!
