Cutting insert, cutting tool, and method of manufacturing machined product

A cutting insert, comprising:

• a first surface comprising a corner part and a first side and a second side each extending from the corner part;
• a second surface connected to the first surface;
• and
• a cutting edge located at a region where the first surface intersects with the second surface, wherein
• the cutting edge comprises:
• a first cutting edge located at the first side,
• a second cutting edge located at the second side, and
• a third cutting edge located at the corner part;
• the third cutting edge comprises:
• a first part connected to the first cutting edge, and
• a second part located between the first part and the second edge;
• the first cutting edge and the third cutting edge are provided with a honing in a front view of the first surface;
• a honing width of the first cutting edge is larger than a honing width of the third cutting edge;
• and
• a honing width of the second part decreases as approaching the second cutting edge.