Bunuel
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 [ 16.87 KiB | Viewed 36659 times ]
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.