In the figure, O is the center of the circle of radius 3, an

Question

2014-06-24_1857.png In the figure, O is the center of the circle of radius 3, and ABCD is a square. If angle AOP = x and the side BC of the square is tangent to the circle, then what is the area of the square ABCD ? (1) PC = 3 (2) x = 60

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=23504 
 In the figure, O is the center of the circle of radius 3, and ABCD is a square. If angle AOP = x and the side BC of the square is tangent to the circle, then what is the area of the square ABCD ?

You can solve this question without actually computing anything there.

(1) PC = 3 --> the length of OC, which is the hypotenuse in triangle BCO, equals to OP + PC = radius + PC = 3 + 3 = 6. Thus we know the lengths of the two sides (OB and OC) in that triangles which enables us to find the third one, BC. Since BC is the side of the square then its area is BC^2. Sufficient.

(2) x = 60. Triangle BOC is 30-60-90 right triangle. We know one of the sides there (BO), hence we can find BC. Since BC is the side of the square then its area is BC^2. Sufficient.

Answer: D.

sahil7389 · Answer

pc=3 then by pythagores theorem you can calculate the one side of square and there by area.
x=60 by tan formula= tan(angle)= p/b you can calculate one side of square and there by area. 
so both independently give you answer.

evdo · Answer

Could you explain more about finding the length of BC using tan(60)?

Bunuel · Answer

You don't need trigonometry for the GMAT. Every GMAT geometry question can be solved without it. Check my post above.

KarishmaB · Answer

When one angle of a right triangle is 60 degrees, we know that the third angle will be 30 degrees. 
In a 30-60-90 triangle, the ratio of the sides is always  1:\sqrt{3}:2  (the side opposite 30, opposite 60 and opposite 90 respectively).
So if you know any one side, you know the other two too.

In triangle BOC, BO = 3 (side opposite 30 degree angle). 
So BC (side opposite 60 degree angle) is  3*\sqrt{3} .

Area of square = BC^2 = 27

Tan 60 does the same thing. Tan 60 is  \sqrt{3}  so it gives that BC =  3*\sqrt{3}

In the figure, O is the center of the circle of radius 3, an

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards