I would use a vector image editor instead. Photoshop could do it, but it's like using a hammer to screw in a nail. Photoshop only has very basic vector capabilities in comparison to proper vector image editing software.
Although Illustrator could be used to do this, it is probably easier in Inkscape, since it has a Polygon tool, with a rounding option, which not only rounds the corners but also curves the edges.
Update: The above example was made using Inkscape 0.48. In the most recent version of Inkscape 0.92 the polygon tool works somewhat differently, in that rounded triangles have no nodes at the vertices, so there are a couple of extra steps required.
When you draw the triangle, adjust it to the desired roundness, then click Path > Object to Path, then Extensions > Modify Paths > Add Nodes, using the setting shown below. This will create additional nodes at the vertices for placing the circles accurately with snapping.