Let the three points A,B,C be the vertices of a moving spherical triangle on the surface of a sphere. The triangle moves so that while the vertices A,B remain fixed, the angle BCA at the vertex C stays constant. What is the locus of the moving vertex C? Is there a special name for the curve traced out by C? If A,B,C were the vertices of a plane triangle, the corresponding locus would be the arc of a circle. I have made some calculations, which-if they do not contain errors-lead me to believe that, in the spherical case, the locus I am seeking is not the arc of a small circle (on the sphere). But, if so, I do not know what type of curve it is.