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Perpendicular (Posted on 2012-12-26) Difficulty: 3 of 5
Let ABC be a triangle and D the foot of the altitude from A. Let E and F lie on a line passing through D such that AE is perpendicular to BE, AF is perpendicular to CF, and E and F are different from D. Let M and N be the midpoints of the segments BC and EF, respectively. Prove that AN is perpendicular to NM.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.3333 (3 votes)

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re(2): Possible approach (Spoiler) Comment 5 of 5 |
(In reply to re: Possible approach (Spoiler) by Harry)

Maybe it is too much of a leap, Harry.

As far as I can reconstruct from my diagram, I actually started with the 3 point circle on A,M,N first, then checked that AM was its diameter (which seemed pretty likely given that D is on the same circle and ADM is a right angle). I thought that was probably enough, but if it isn't I'm quite happy to concede the point!

 

Edited on December 27, 2012, 3:36 pm
  Posted by broll on 2012-12-27 15:28:25

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