Similar Triangles with Restrictions
Inspired by a post at the Futility Closet, http://www.futilitycloset.com/2016/01/11/straight-and-narrow-4/, and then quickly generalized when exposed to the MTBoS. (Math-Twitter-Blog-o-Sphere).
Thanks to: John Armstrong, Matt Enlow, Simon Gregg, and Henri Picciotto for the brain stretching. Cf. https://twitter.com/mathhombre/status/687011086567104520 for the twitter conversation.