Let ABC be an acute-angled triangle, Γ its circumcircle and M the midpoint of BC. Let N be a point in the arc BC of Γ not containing A such that ∠NAC=∠BAM. Let R be the midpoint of AM, S the midpoint of AN and T the foot of the altitude through A. Prove that R, S and T are collinear. geometrycircumcirclehardCyclicconcurrency