MathDB
the Lemoine point is the midpoint of the altitude

Source: 2023 Viet Nam math olympiad for high school students D1 P6

March 25, 2023
geometry

Problem Statement

a) Given a triangle ABCABC with ∠BAC=90∘\angle BAC=90^{\circ} and the altitude AH(HAH(H is on the side BC).BC). Prove that: the Lemoine point of the triangle ABCABC is the midpoint of AH.AH.
b) If a triangle has its Lemoine point is the midpoint of 11 in 33 symmedian segments, does that triangle need to be a right triangle? Explain why.
Back to ProblemsView on AoPS