Let E be the midpoint of side AB of square ABCD. Let the circle through B with center A and segment EC meet at F. what is the ratio of $CE/EF$?
Interestingly enough, it seems like setting a point G, where G is the midpoint of line BC, can form a line DG that intersects perpendicularly with line CE and intersects exactly at F. Should this be true, then similar triangle ratios can be used to determine the ratio CE/EF. How should I show that this is true? Or is there a better way to solve this problem?