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

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 amFollowed by: 21 members; Thanked: 230 times

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 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; 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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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Tue Oct 25, 2011 10:11 am

Please find the attachment as requested

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