MathDB
triangle is not isosceles

Source: 2007 Korean MO, 2nd Round, P.M.

August 18, 2007
geometrycircumcirclegeometry unsolved

Problem Statement

ABC ABC is a triangle which is not isosceles. Let the circumcenter and orthocenter of ABC ABC be O O, H H, respectively, and the altitudes of ABC ABC be AD AD, BC BC, CF CF. Let K≠A K\neq A be the intersection of AD AD and circumcircle of triangle ABC ABC, L L be the intersection of OK OK and BC BC, M M be the midpoint of BC BC, P P be the intersection of AM AM and the line that passes L L and perpendicular to BC BC, Q Q be the intersection of AD AD and the line that passes P P and parallel to MH MH, R R be the intersection of line EQ EQ and AB AB, S S be the intersection of FD FD and BE BE. If OL \equal{} KL, then prove that two lines OH OH and RS RS are orthogonal.
Back to ProblemsView on AoPS