A little puzzle: "Dear lazyweb,

I have a square with side length 3 - x. The sides are labelled A, B, C, and D, going around clockwise. There's a point p on A and a point q on B, such that the distance between p and q is 2. We label the intersection of C and D as r. There is a point on pq which we label s, such that rs is perpendicular to pq. The distance between r and s is x + 1. If the angle between rs and D is a, solve for x in terms of a. Bonus points if you convert from polar to cartesian coordinates.

Yes, there's a real motivation for this problem. I'm having trouble solving it though, I've always sucked at geometry."

(Via bramcohen.)