Nine Point Circle

Center of the nine-point circle lies on the Euler's line and it's the midpoint of Orthocenter and Circumcenter.
Radius of the nine-point circle is half of the Circumradius of the original triangle.


This proof uses the facts that OM1, i.e. distance from Circumcenter O to line BC(i.e. its midpoint) is R.cosA whereas AH = 2R.cosA where R = circumradius and H = Orthocenter.
Proof video.




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