# The Circle of Euler

Submitted by Structure on Sat, 12/29/2007 - 23:47.

These 9 points are on the circle of Euler:

- the middles of the sides: A1, B1 and C1

- the projections of A, B and C on the sides: A2, B2 and C2

- the middles of AH, BH and CH: A3, B3 and C3

When a point M is on the circumcircle of ABC,we have OM=R

The midsegment ABC parallel to OM is wN =

w is the middle of OH,so it is on Euler line.

The center of the circle is the middle of OH.