TeamGMATIFY wrote:

Bunuel wrote:

If a circle is inscribed in an equilateral triangle, what is the area of the triangle NOT taken up by the circle?

(1) The area of the circle is 12π

(2) The length of a side of the triangle is 12

Following is the formula that tells the relation between the radius of the circle and the side of the triangle:

r = a * (\(\sqrt{3}\)/ 6)

So if we have either of the side or the radius, we can find the other thing.

The relation can be found by using the figure below:

Attachment:

circle in triangle.JPG

Statement 1: The area of the circle is 12π

We can find the radius of the circle and hence the side of the triangle and the corresponding area

Therefore we can find the difference between the areas

SUFFICIENT

Statement 2: The length of a side of the triangle is 12

We can find the radius of the circle and hence the area of the circle

Therefore we can find the difference between the areas

SUFFICIENT

Option D

NOTE: We do not need to find the area. There is not need to do the calculations.

HI

TeamGMATIFY,

Actually I already learnt this formula but haven't tried to figure it out the logic behind this.

The figure provided by you makes a triangle of 30-60-90 = 1x : Root 3* x : 2x

So the opposite length of side 30 degree angle --> R

=> 1x= R or x=R

And opposite length of side 60 degree angle--> A/2

=> root 3 * x = A/2

By this I am getting relation as --

R= A / (root 3 * 2) which is not the same

Can you please assist..??

_________________

Thanks and Regards,

Prakhar