May 11–May 17, 2010
Problem
Consider an equilateral triangle ABC, and let M be any point
on the side BC, but different from B and C.
Consider the point N such that BMN is equilateral, and
N d$
not lie in BA.
Let P, Q, and R be the midpoints
of AB, BN, and CM respectively. Our guess is that
PQR is equilateral. Can you prove it?
Solution
List of solvers
Lloyd Sakazaki, Aparna Khare, Congpa You, Peiyush Jain, Kevin Sonnanburg, Mukund Tirumalai, William Lalum, Brad Heller, Dean Menezes, Jonathan Cross, Tien Nguyen, Bai Li, Crispin Pereira.
Crispin Pereira wins the prize!