Let ABC be an acute triangle, let H and O be its orthocentre and circumcentre, respectively,
and let S and T be the feet of the altitudes from B to AC and from C to AB, respectively.
Let M be the midpoint of the segment ST, and let N be the midpoint of the segment AH. The line
through O, parallel to BC, crosses the sides AC and AB at F and G, respectively. The line NG
meets the circle BGO again at K, and the line NF meets the circle CFO again at L. Prove that
the triangles BCM and KLN are similar. geometryconfig geoRMM Shortlist