MathDB
Area ratio inequality

Source: China TST 2003

June 29, 2006
geometryratioinequalitiesanalytic geometrylinear algebramatrixgeometry unsolved

Problem Statement

In triangle ABCABC, the medians and bisectors corresponding to sides BCBC, CACA, ABAB are mam_a, mbm_b, mcm_c and waw_a, wbw_b, wcw_c respectively. P=wa∩mbP=w_a \cap m_b, Q=wb∩mcQ=w_b \cap m_c, R=wc∩maR=w_c \cap m_a. Denote the areas of triangle ABCABC and PQRPQR by F1F_1 and F2F_2 respectively. Find the least positive constant mm such that F1F2<m\frac{F_1}{F_2}<m holds for any △ABC\triangle{ABC}.
Back to ProblemsView on AoPS