MathDB

4

Part of 2006 German National Olympiad

Problems(1)

A point far, far away...

Source: Germany 2006 - Problem 4

12/9/2022
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.
TriangledistanceSegmentgeometry