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 $\Delta$ ABC,we have OM=R
The midsegment $\Delta$ ABC parallel to OM is wN = $\frac{1}{2}R$
w is the middle of OH,so it is on Euler line.
The center of the circle is the middle of OH.