Khan/khan-exercises — pull request #161305 by simonjtyler (2014-01-24 08:39:03+00:00)
Title: New validator for parallel line exercise in constructions_1

There were a lot of [issues](https://github.com/Khan/khan-exercises/search?q=Compass+constructions+1+problem%3Dparallel&type=Issues) regarding the problems with this exercise, especially about it not accepting valid constructions differing from that shown in the hint. For example [issue:155778](https://github.com/Khan/khan-exercises/issues/155778).

There seem to be three basic ways of solving the compass-straightedge problem:
*Given a line L and a point P not on that line, construct a line though P that is parallel to L.*
1. Choose two points, A and B, on L and then use A, B, P to create a parallelogram. (This can be done using only compasses - no need to draw the unneeded sides.)
2. Draw a line from P that crosses L. Transfer the angle created to P. (This is the method used in excellent hint)
3. Construct two perpendicular lines. Messy, but it works!
The common features of these and all(?) good parallel constructions have are
1) Require that there is one parallel line through P. (i.e., the problem is solved!)
2) There are at least two circles with an intersection point on that line. (Some construction has been used to create the line.)
So these are the two things I've added checks for. Hopefully this covers all reasonable constructions and is not too easily/often gamed.