Circle GEO (1 Viewer)

[CrashOveride]

the altitudes AD and BE of triABC meet at F. L, M, N are the midpoints of BC, AF and AB respectively. LN and BE intersect at K. Prove that LNM = 90degrees

 

[coca cola]

umm tricky question... let me have a think.

 

[coca cola]

looks like i won't be figuring this out any time soon, i see a cyclic quad and a couple of similar triangles, but still can't get the angle.

this hurts my eyes...

 

[Estel]

See attachment:
I tried posting numerous times but BOS keeps covering it unless you quote...

Note: non circle geometry solution, I will try finding a proper answer tomorrow when I'm not so tired.

 

[Estel]

Are you sure this is circle geometry? I see a few cyclic quadrilaterals but there's not really much else I can find...