Is a triangle, with one side of length 12, inscribed in a ci

[Max@Math Revolution]

[GMAT math practice question]

Is a triangle, with one side of length 12, inscribed in a circle a right triangle?

1) The area of the circle is 36Ï€.
2) The circumference of the circle is 12Ï€.

[Max@Math Revolution]

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.



If a side of a triangle is the diameter of its circumscribed circle, then the triangle is a right triangle.

Condition 1)
A circle with area 36 π has radius 6 and diameter 12. So, the answer is 'yes' and condition 1) is sufficient.

Condition 2)
A circle with circumference 12 π has diameter 12. So, the answer is 'yes' and condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

Note that if conditions 1) and 2) yield the same information, Tip 1 of the VA method tells us that D is most likely to be the answer.