mikemcgarry wrote:
ABC is an equilateral triangle, and point D is the midpoint of side BC. A is also a point on circle with radius r = 3. What is the area of the triangle?
Statement #1: The line that passes through A and D also passes through the center of the circle.
Statement #2: Including point A, the triangle intersects the circle at exactly four points.
Geometry is an astonishingly beautiful topic, and the GMAT DS is full of it. This question is from a collection of 10 challenging DS Geometry questions. For the others, as well as the OE for this problem, see:
GMAT Data Sufficiency Geometry Practice QuestionsMike
Information given:- D is midpoint of side BC, and ABC is an equilateral triangle.
A is a point on circle with radius 3.
Question asked:- area of triangle?
\sqrt{3}/4 side^2 (we can also find the area if we would know height)
Statement #1: The line that passes through A and D also passes through the center of the circle.
Now keeping point A on the center, while AD passing through the center. We can have AD as the diameter or part of diameter.
If AD is the diameter, we can find the area since radius is given to us. But if AD is part of the diameter, then we would not be able to find the area.
Statement #2: Including point A, the triangle intersects the circle at exactly four points
There can be many different triangles intersecting at 4 points, including point A. Not sufficient.
Combining statement 1 and 2- the only case when AD passes through center and the circle intersects at 4 points is when AD is diameter.
And, hence we can find the area of the triangle.
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