rommysingh wrote:In the figure, ABC is an equilateral triangle, and DAB is a right triangle. What is the area of the circumscribed circle?
(1) DA = 4
(2) Angle ABD = 30 degrees
Inscribed ∠DAB = 90 degrees.
An inscribed angle of 90 degrees intercepts the diameter.
Thus, DB is the diameter of the circle.
Inscribed angles that intercept the same arc are equal.
Inscribed angles ∠ADB and ∠ACB both intercept arc AB.
Thus, ∠ADB = ∠ACB.
Since ∆ABC is equilateral, ∠ACB = 60 degrees, implying that ∠ADB = 60 degrees.
The result, as shown above, is that both ∆ADE and ∆AEB are 30-60-90 triangles.
Since the two triangles share side AE, if we know one side of either triangle, we can determine the lengths of all the other sides -- including DE and EB, which form the diameter.
The length of diameter DB will allow us to determine the area of the circle.
Question rephrased: What is the length of one side of either ∆ADE or ∆AEB?
Statement 1: AD = 4.
Sufficient.
See below:
Statement 2: ∠ABD = 30.
No new information.
The question stem itself implies that ∠ABD = 30.
Insufficient.
The correct answer is
A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
