SMO 2008 q2
Source: SMO 2008, open, 2nd round
March 30, 2018
geometry
Problem Statement
in the acute triangle .
M is a point in the interior of the segment AC and N is a point on the extension of segment AC such that MN=AC.
let D,E be the feet of perpendiculars from M,N onto lines BC,AB respectively
prove that the orthocentre of lies on circumcircle of