> When the brute search fails, an extra geometric construction is randomly added (like adding a midpoint of a certain line) to see if brute search using that ex

> When the brute search fails, an extra geometric construction is randomly added (like adding a midpoint of a certain line) to see if brute search using that extra raw material might work That's exactly how I was taught geometry in school and I hated it with my all guts. Only after making it into the math department of the university I learned to do it properly and to enjoy it.