MathDB
perpendicular wanted, midpoint, angle bisector, parallel, median related

Source: 2000 Argentina OMA L3 p2

June 15, 2020
geometryangle bisectormedianparallelperpendicular

Problem Statement

Given a triangle ABCABC with side ABAB greater than BCBC, let MM be the midpoint of ACAC and LL be the point at which the bisector of angle B\angle B intersects side ACAC. The line parallel to ABAB, which intersects the bisector BLBL at DD, is drawn by MM, and the line parallel to the side BCBC that intersects the median BMBM at EE is drawn by LL. Show that EDED is perpendicular to BLBL.