Cat Food Sharing
There are two cats that share a single can of food at each meal. The cats are very finicky and get angry if their portions are unequal. The owner is finicky too, and doesn’t like dirtying dishes when he divides it up. To split the food, then, he upends the open can of food onto a flat plate, then carefully lifts the can off, leaving a perfectly formed cylinder of cat food. He then uses the thin and razor-sharp circular edge of the can to carefully cut the food into two exactly equal portions, one of which is shaped like a crescent moon, the other a cat's eye (or mandorla) as shown in the diagram below (the dotted circle represents the can used to cut the food).
There are two objectives:
- Determine how far he needs to offset the empty can in order to bisect the food equally. Find the distance between the center of the can and the center of the food relative to the radius (to make things simple, assume the radius of the can is 1 unit).
- Find the angle (in degrees) formed inside the two radii that connect the center (of either circle) to the points of intersection of the two circumferences.