Superabrasive inserts including an arcuate peripheral surface

A subterranean drill bit comprising:

• a bit body;
• at least one superabrasive gage insert, the at least one superabrasive gage insert comprising:
• a superabrasive layer bonded to a substrate at an interface, wherein the superabrasive layer includes a central substantially planar surface, a peripheral side surface and an arcuate peripheral surface extending between the central substantially planar surface and the peripheral side surface;
• wherein a cross section of the arcuate peripheral surface comprises a substantially circular arc and wherein the substantially planar surface is tangent to the substantially circular arc at an intersection between the substantially circular arc and the substantially planar surface;
• wherein a tangent reference line to the substantially circular arc extending from an intersection between the peripheral side surface of the superabrasive layer and the substantially circular arc forms an acute angle with the peripheral side surface;
• wherein, during intended operation of the drill bit, the drill bit rotates about a defined axis, and wherein the at least one superabrasive gage insert rotates about the defined axis along a substantially circular path with the substantially planar surface being oriented substantially tangent to the substantially circular path.