Bile is released into the in response to the ingestion of fat

The answer is duodenum (upper part of small intestine)

Bile is produced in the liver, stored in Gall bladder, released to duodenum through bile duct.

The main function of bile is to physical digest fat, which means this digestion does not require enzymes. It only break fats into numerous oil droplets, instead of turning them into fatty acid and glycerol, which is what enzyme lipase does. Bile can only help increase the surface area of fat, to make chemical digestion a lot more efficient. The product from bile digestion is not the final form of fat that the body absorbs.

Called for cell.