Question: 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?

(1) The line that passes through A and D also passes through the center of the circle.
(2) Including point A, the triangle intersects the circle at exactly four points.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“ABC is an equilateral triangle, and point D is the midpoint of side BC” - is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solutions and Explanation

Approach Solution : 1

Statement (1) :

It states that the circle's center is intersected by the line that runs through A and D.
Triangle's area is not fixed because altitude can be any length between 0 and 6.
Therefore this statement is not sufficient.

Statement (2) :

It states that the triangle crosses the circle exactly four times, counting point A.
As a result, numerous triangles are possible to form.
Therefore this statement is not sufficient.

Combined:

There is only one way in which the triangle's altitude will be adequate when AD = 6
This is sufficient.

Correct Answer: (C)

Approach Solution : 2

From the picture given above, it is clear that both the statements alone are not sufficient.

Correct Answer: (C)

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