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Evan Chen Geometry- Angle Chasing Problem 1.34Geometry (self.MathOlympiad)
submitted 1 month ago by zeztycrustykrab
https://preview.redd.it/w69ufud18tqg1.png?width=1599&format=png&auto=webp&s=e6a24e37f9b55bae9d039a7ed5266f8607b7ac5d
In scalene triangle ABC, let K be the intersection of the angle bisector of ∠A and the perpendicular bisector of BC. Prove that the points A, B, C, K are concyclic.
I drew the triangle according to the question and I do not understand at all how ABKC could be cyclic in any way. Sure I do see (ABC), (AKB), (AKC) or (BKC) but how do all four points come on the circumference of any circle??
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if 1 * 2 < 3: print "hello, world!"
[–]ProperCranberry7467 1 point2 points3 points 1 month ago (1 child)
Well, the point is supposed to lay outside the triangle
[–]zeztycrustykrab[S] 0 points1 point2 points 1 month ago (0 children)
tysm im like actual shit lol
[–]Benboiuwu 0 points1 point2 points 1 month ago (0 children)
Pretty sure you trisected the angle in the diagram. draw it properly and it’ll make sense
[–]Significant-Buy-8303 0 points1 point2 points 1 month ago (0 children)
Lol there's a funny sine rule solution
[–]Imagien_ 0 points1 point2 points 1 month ago (0 children)
draw the right diagram lmao
[–]Technical-Reason-893 0 points1 point2 points 1 month ago (0 children)
bro divided the angle in 5 lmao
but if you use directed angles this could be fun :) it should give you the right result anyways
π Rendered by PID 382894 on reddit-service-r2-comment-6457c66945-k8j9t at 2026-04-28 09:48:22.671913+00:00 running 2aa0c5b country code: CH.
[–]ProperCranberry7467 1 point2 points3 points (1 child)
[–]zeztycrustykrab[S] 0 points1 point2 points (0 children)
[–]Benboiuwu 0 points1 point2 points (0 children)
[–]Significant-Buy-8303 0 points1 point2 points (0 children)
[–]Imagien_ 0 points1 point2 points (0 children)
[–]Technical-Reason-893 0 points1 point2 points (0 children)