Let A1 be the point in the circumcircle such that AA1 and BC are parallel. Let A2 be the point in the circumcircle such that A1A2 and the A-altitude are parallel.  Define analogously B1, C1, B2, C2. The circles {OA1A2}, {OB1B2}, {OC1C2} intersect at a point in the Euler line.