I'm helping to run a math competition at my school and we pulled a problem from this site that we are having trouble solving.
Eight circles of radius 1 have centers on a larger common circle and adjacent circles are tangent. Find the area of the common circle. See the illustration below.
- Not sure. It has been a long time since I've done this kind of math.
if it helps, the answer is supposed to be
my colleagues and I can't figure out how to come to that answer. It's probably something simple.
edit: I tried to solve it by inscribing an octagon, and then finding the distance from the center of the octagon to the side of the octagon. but I got 1 + sqrt(2) as the radius... rather than the 2*sqrt(2+sqrt(2))