Pool Party Problem
Alice, Bobby and Carla are swimming in a circular pool with area \(100\pi\) ft\(^2\). All the kids are hanging onto the side of the pool when Alice's dad throws a beach ball into the pool. The kids all leave at the same time and race towards the ball. If Bobby swims twice as fast as Alice, and Carla swims twice as fast as Bobby, what is the closest that Alice's dad can throw the ball to the center of the pool such that all three kids reach the ball at the same time?
Express your answer as the distance between the center of the pool and the ball.