In the diagram above, A is the center of the circle, angle ABD = 90°

Question

https://gmatclub.com/forum/download/file.php?id=26289 In the diagram above, A is the center of the circle, angle BAD = 90°, and the area of triangle ABD is 24\sqrt{3} . What is the area of the circle? (1) AB = 12 (2) AD = CD Kudos for a correct solution . gdrtq_img1.png

Lucky2783 · Answer

if AB is given we can find AD and hence area of circle . option A is sufficient.

option B : please refer the attached image .

we can find all the sides of ACE as BC=AC=R.
finally will get an expression in Something* (R^2)  =  24 * \sqrt{3}  Sufficient.

Harley1980 · Answer

1) We know that this is right triangle. We know its area and one of the side AB so we can find AD
 \frac{(AB * AD )}{2}=24 * \sqrt{3}

AB = 12

so  AD = 4\sqrt{3}

AD is a radius so we can find area of circle.
Sufficient

2) AD = CD so triangle ADC equalateral and angle ADC = 60 degrees
Ratio of sides in triangle  ABD = 1:\sqrt{3}:2

So  AB = R\sqrt{3}  and  AD = R

\frac{(R\sqrt{3} * R )}{2}=24 * \sqrt{3}

R^2\sqrt{3}=48 * \sqrt{3}

R=4 \sqrt{3}

R is a radius so we can find area of circle.
Sufficient

Answer is D

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

In order to find the area of the circle, we would need the radius, AD.

Statement #1:  AB = 12. Notice that AD is the base of triangle ABD. AB is the height, now known, and we know the area. If we know the height and the area, we can find the base by A = 0.5*bh. Therefore, we can find AD, which would allow us to find the area of the circle. This statement, alone and by itself, is sufficient.

Statement #2:  We know that AD = AC, because all radii of a circle are equal. If CD also equals these two, then ACD is an equilateral triangle. That means that the angle ADC = 60°, which means that triangle ABD is a 30-60-90 triangle. If AD = x is the base, then this times the square-root of 3 is the height, and we could create an equation because we know the area:

24\sqrt{3}=\frac{1}{2}*x*x\sqrt{3}

This is an equation we could solve for x, which would allow us to find the area of the circle. This statement, alone and by itself, is sufficient.

Answer = (D)

mperalta · Answer

How do you know AD is a radius though? It doesn't specify that anywhere in the question.

patrapan · Answer

A is the center of the circle so AD has to be radius

mperalta · Answer

Yeah, but how do you know it "dies" right at the circumference? Does the black dot in the diagram mean that it does?

bumpbot · Answer

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In the diagram above, A is the center of the circle, angle ABD = 90°

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