MathDB
A point far, far away...

Source: Germany 2006 - Problem 4

December 9, 2022
TriangledistanceSegmentgeometry

Problem Statement

Let DD be a point inside a triangle ABCABC such that ∣AC∣−∣AD∣≥1|AC| -|AD| \geq 1 and ∣BC∣−∣BD∣≥1.|BC|- |BD| \geq 1. Prove that for any point EE on the segment ABAB, we have ∣EC∣−∣ED∣≥1.|EC| -|ED| \geq 1.
Back to ProblemsView on AoPS