# what is the aera of the circle with center E?

• Aug 17th 2012, 04:14 PM
slapmaxwell1
what is the aera of the circle with center E?
ok so the problem wants me to find the area of the circle with center E. it was pretty easy to figure out that the diameter of the small circle was 6. once i figure out the diameter i can use that relationship to say that the area of the circle with center A and center C is 36pi. but this is where im stuck. im not sure how im supposed to use these relationships to figure out the area of the circle with center E. any thoughts or help would be greatly appreciated.
Attachment 24534
• Aug 17th 2012, 04:42 PM
richard1234
Re: what is the aera of the circle with center E?
$BC = 3$, so $AC = 6$.

It is easy to show that triangle ACD is equilateral (since the side lengths are all radii of either circle w/ center A or C). Using some 30-60-90 triangles, $BD = 3 \sqrt{3}$, so $ED = 2BD = 6 \sqrt{3}$.

ED is a radius of the circle with center E, so the area of this circle is

$\pi (6 \sqrt{3})^2 = 108 \pi$, answer choice (C).