Select the orange line layers and go Layer>Group Layers. With the group selected, hit the Add Layer Mask button and create a mask. Hit it another time to make a vector mask. Select the vector mask from the white circle layer. Hit Command+C to copy. Select the vector mask on the "lines" group then hit Command+V to paste. Hit Command+T and scale down the path slightly so there is a little space between the path and the edge of the gray circle.