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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 am; Location: Chennai, India; Thanked: 206 times; Followed by:43 members; GMAT Score:640

Garden

by GmatKiss » Sat Oct 22, 2011 2:08 am

The circular base of a planter sits on a level lawn, and just touches two straight garden walls at points W and Y. The walls come together at point X, which is 15 inches from the center of the planter. What is the area of the base of the planter?

(1) Both points Y and W are 9 inches from the center of the planter

(2) Point W is 12 inches from point X

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 22, 2011 2:08 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

by shankar.ashwin » Sat Oct 22, 2011 2:14 am

Should be D IMO.

Both statements give you the radius of the circle from which area could be calculated.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sat Oct 22, 2011 2:51 am

GmatKiss wrote:The circular base of a planter sits on a level lawn, and just touches two straight garden walls at points W and Y. The walls come together at point X, which is 15 inches from the center of the planter. What is the area of the base of the planter?

(1) Both points Y and W are 9 inches from the center of the planter
(2) Point W is 12 inches from point X

This question is based on the concept that tangents of a circle at any point is perpendicular to the radius drawn from that point. Now, the line joining the center of the circle with W and Y is nothing but the radii of the circle which is perpendicular to WX and WY at the point W and Y respectively.

Now statement 1 simply gives us the radius of the circle. Hence, we can determine the area.

And statement 2 tells us WX = 12 and from the question itself OX = 15, where O is the center. As WXO will be a right-angled triangle, we can easily derive the length of WO as âˆš(15Â² - 12Â²) = 9, which is radius of the circle.

Hence, both statements individually tells us the length of the radius of the circle.

The correct answer is D.

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