Find the locus of points $P$ in an equilateral triangle $ABC$ for which the square root of the distance of $P$ to one of the sides is equal to the sum of the square root of the distance of $P$ to the two other sides.
Problem
Source: Iran TST 2011 - Day 3 - Problem 1
Tags: geometry proposed, geometry
mahanmath
14.05.2011 19:31
http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1030119&sid=af993120c9ba8099664370626a7153e4#p1030119 Thank you dear proposer for your creativity !
yetti
14.05.2011 21:14
The problem or its variants have been posted at least 4 times in past: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=106446 (Aug. 2006) http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=187662 (Feb. 2008) http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=267668 (Mar. 2009) http://www.artofproblemsolving.com/Forum/viewtopic.php?f=47&t=388690 (Jan. 2011) mahanmath, your comment was unnecessary and baseless. shoki included reference, where he got the problem. Please refrain from posting similar comments.
shoki
15.05.2011 13:01
@mahanmath : thanks for the link and yes you are right !!! they had a lot of creativity on this one (,too)!!! @yetti : thank you too for the other links.