In a circle O, there are six points, A, B, C, D, E, F in a counterclockwise order such that BD⊥CF , and CF, BE, AD are concurrent. Let the perpendicular from B to AC be M, and the perpendicular from D to CE be N. Prove that AE∥MN.
Source: 2021 Saudi Arabia JBMO TST 1.2
Tags: geometry, hexagon, Cyclic
In a circle O, there are six points, A, B, C, D, E, F in a counterclockwise order such that BD⊥CF , and CF, BE, AD are concurrent. Let the perpendicular from B to AC be M, and the perpendicular from D to CE be N. Prove that AE∥MN.