## problem 5 (elementary) Iranian geometry Olympiad 2017

For students of class 6-8 (age 12 to 14)
abrarfiaz
Posts: 14
Joined: Mon Mar 20, 2017 4:53 pm

### problem 5 (elementary) Iranian geometry Olympiad 2017

In the isosceles triangle ABC (AB = AC), let l be a line parallel to BC through A. Let D be an arbitrary point on l. Let E, F be the feet of perpendiculars through A to BD, CD respectively. Suppose that P, Q are the images of E, F on l. Prove that AP + AQ ≤ AB.

"God made the integers; all else is the work of man."

jayon_2
Posts: 7
Joined: Sat Feb 11, 2017 4:06 pm

### Re: problem 5 (elementary) Iranian geometry Olympiad 2017

Post the problem in some other forum,like AoPS.This forum is dead.

Posts: 120
Joined: Sun Jan 28, 2018 11:43 pm
Location: Bhulta, Rupganj, Narayanganj
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### Re: problem 5 (elementary) Iranian geometry Olympiad 2017

samiul_samin
Posts: 1004
Joined: Sat Dec 09, 2017 1:32 pm

### Re: problem 5 (elementary) Iranian geometry Olympiad 2017

[img]Here is the official solution.[/img
Screenshot_2018-02-02-18-26-21.png

dwipneel
Posts: 4
Joined: Wed Sep 13, 2017 11:18 pm