5.4 Loh. Constructing a Very Special Circle through Six Very Special Points References [1] Quantum Physics Lady. What is wave function collapse? is it a physical event? 2020. URL: http:
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/ / www . quantumphysicslady . org / what is - wave - function - collapse - is - it - a physical-event/ (cited on page 54).
5.4 Constructing a Very Special Circle through Six Very Special Points (ft. weird angle chasing and magical tornadoes) By Vivian Loh ’24 noindent The following proof is the proof of Lemma 3.11 in the book EGMO [1] “The Nine-Point Circle"
We claim that there is a circle passing through the 3 blue points AND the 3 red points, like this: What the heck even is that diagram? First of all, given a triangle, these three blue lines are the altitudes, AKA the lines from opposite corners forming 90 degree angles with the sides.
(Not all sets of 6 points can have a circle drawn through them, for example these 6 points do not.) And these three red points are the midpoints of the sides.
