Given the vertex and the centroid of a triangle , find the locus of vertices such that all the angles of the triangle lie in the interval
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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
Školjka 
and the centroid 
of a triangle 
, find the locus of vertices 
such that all the angles of the triangle lie in the interval ![[40^\circ, 70^\circ].](/media/m/9/a/d/9adb384f374eb62fabd3675b69323b53.png)