Let AaAbAc, BbBcBa, CcCaCb be the orthiac triangles of ABC. Let A1, A2, A3 be the midpoints of AaA, AaAb, AaAc and define cyclically B1, B2, B3, C1, C2, C3. Then:
1) The Euler lines of A1A2A3, B1B2B3, C1C2C3 are concurrent.
2) Their parallels from A, B, C concur at X(74)
3) Their parallels from Aa, Bb, Cc are concurrent
4) The three concurrence points are collinear with the symmedian K.