MathDB
2017 IGO Intermediate P4

Source: 4th Iranian Geometry Olympiad, P4 of intermediate level, P5 of elementary level

September 15, 2017
IGOIrangeometry

Problem Statement

In the isosceles triangle ABCABC (AB=ACAB=AC), let ll be a line parallel to BCBC through AA. Let DD be an arbitrary point on ll. Let E,FE,F be the feet of perpendiculars through AA to BD,CDBD,CD respectively. Suppose that P,QP,Q are the images of E,FE,F on ll. Prove that AP+AQ≤ABAP+AQ\le AB
Proposed by Morteza Saghafian
Back to ProblemsView on AoPS