IMO Shortlist 1966 problem 55
Dodao/la:
arhiva2. travnja 2012. Given the vertex
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
and the centroid
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
of a triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
, find the locus of vertices
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
such that all the angles of the triangle lie in the interval
%V0
Given the vertex $A$ and the centroid $M$ of a triangle $ABC$, find the locus of vertices $B$ such that all the angles of the triangle lie in the interval $[40^\circ, 70^\circ].$
Izvor: Međunarodna matematička olimpijada, shortlist 1966