Coordinate geometry and circles
(This is Glen.) As you may have noticed from my previous posts, my go-to method for approaching geometry problems is bashing, normally with coordinates. Anyone who's tried to bash a problem (especially with coordinates) would have probably found out the hard way that circles generally lead to trouble, but years of bashing have led me to devise some tricks to get around this. I'll be writing about them below, along with, as far as possible, some examples which I remember bashing. I'm not typing out solutions for the sake of my sanity, and besides, I think there is value in actually working through the algebra. Instead, I'm just going to sketch an approach which I think is the most efficient. Introduction Bashing apologia Before I get lynched by the Synthetic Mafia, I should probably provide some justification for this post. Why bash? As a cynical member of the Synthetic Mafia might tell you, it's what immoral people do when they fail in thinking about a problem geom
