## If the center of a circle lies on a smaller circle...

##### This topic has expert replies
Moderator
Posts: 1988
Joined: 15 Oct 2017
Followed by:6 members

### If the center of a circle lies on a smaller circle...

by BTGmoderatorLU » Thu Mar 15, 2018 2:47 pm 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!

GMAT Instructor
Posts: 15533
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1900 members
GMAT Score:790
by GMATGuruNY » Thu Mar 15, 2018 4:07 pm
LUANDATO wrote: 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
Let the diameter of the larger circle = 4, implying that the diameter of the smaller circle = 2.
Area of the larger circle = Ï€rÂ² = Ï€(2)Â² = 4Ï€.
Area of the smaller circle Ï€rÂ² = Ï€(1)Â² = Ï€.
Area of the unshaded portion = larger circle - smaller circle = 4Ï€ - Ï€ = 3Ï€.
Thus:
(unshaded portion)/(larger circle) = (3Ï€)/(4Ï€) = 3/4.

Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

### GMAT/MBA Expert

GMAT Instructor
Posts: 6362
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:26 members
by [email protected] » Fri May 24, 2019 3:14 pm
BTGmoderatorLU wrote: 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

We can let the radius of the smaller circle = 1 and thus the radius of the larger circle = the diameter of the smaller circle = 2. The area of the smaller circle is Ï€ and the area of the larger circle is 4Ï€. Therefore, the area of the shaded region is 4Ï€ - Ï€ = 3Ï€ and hence the area of the shaded region is 3Ï€/4Ï€ = 3/4 of the area of the larger circle.