Andrew Stacey @mathforge.org · Aug 5 I have a query about one of @catrionaagg.bsky.social 's puzzles. The goal is the area of the red quarter circle. I have a solution that *doesn't* use the semi-circle. Am I missing something, or is that semi-circle irrelevant? #geometrypuzzles notes.mathforge.org/notes/publis...
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I think I probably just put it there because I liked the look of equally-spaced dots along the hypotenuse.
(NB There's a link to the original post on twitter. I /presume/ that this is discussed there but I no longer have a twitter account so cannot follow links within twitter. So someone who still has such an account could just look it up. But, it'd be nicer to have that discussion here not there!)
I’d like to add to the conversation that “extra” information in a problem is a good thing for students to grapple with.
My gut says the triangle is already determined by the information given without the semicircle. The fact that the point on the hypotenuse nearest to the opposite vertex is one third of the way down the hypotenuse should determine the triangle up to similarity, the the 2's provide scale.
I don't see what information that semicircle is providing - nothing is labeled on it. Could it be a misprint maybe, where they wanted the area in red under that semicircle or something?
It seems to me that we don't know anything about the semicircle except its point of tangency, so I don't see how we *could* use it? Looks to me just like just a cute way to show that the point of tangency if the quarter circle is a third of the way there? But maybe I'm missing something...