I expect student solution methods to end up using similar triangles. Here's a solution method I did not expect:
Me: "Show me what you got."
Student: "Well, I drew perpendiculars to the wall from the Ball and the Hole.
Student: "Well, I measured it and all the proportions check out."
Me: "Hmm. I don't know why that would be true. Can you try it with a different location of the ball and the hole and see if it still works?"
Student: "Did I just come up with something that works and you didn't know about it?!"
Me: "Maybe, but you'll need to convince me that it might be true. Maybe you just got lucky with your ball and hole placements."
Student: "Okay I'll check"
The student tried another variation and it still worked. After school, I put the situation into a Geogebra file and it does seem to hold true. At least I cant' find a counter example. So, here's the question, are triangle AFC and triangle BFD similar? Why or why not?