If the middle S is a chord of a circle, then the end S can be a chord going either way on that circle and the angle A will be equal either way. So I'm guessing X is the circumcircle. --ms On 06-Apr-15 15:51, James Propp wrote:
Back about 30-40 years ago, I posed a problem in Mathematics Magazine (or maybe the Monthly) asking whether any triangle could be linked to a non-congruent similar triangle via a sequence of triangles, each "SSA-congruent" to the one before and the one after. There was a cute solution that pointed out that this is impossible because two SSA-congruent triangles have the same X, where X was some triangle statistic (like perimeter, inradius, or circumradius, but slightly less well-known) that scales linearly under similarity.
Can anyone (a) figure out what X was, or (b) locate my problem and the solution?
Jim Propp
PS: In my original submission I proposed the term "ASS-congruent", which struck me as both more pronounceable and more apt, but the stodgy problems editor who reigned at the time deemed this too vulgar. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun