For a given triangle ABC, we define the Nine Point Circle as the circumcircle of the medial triangle of ABC and prove that it contains the nine key points: The midpoints of the sides of ABC, the midpoints of the segments AH, BH, and CH where H is the orthocenter of ABC, and the feet of the altitudes of ABC.
Proof writeup: https://drive.google.com/file/d/1LMl5_YKUjvsBHzFsQwMdhU9djhJsJYs8/view?usp=sharing
Geogebra Illustration: https://www.geogebra.org/geometry/dmtbydr5
