The way three medians of a triangle can form a triangle, whose area is 3/4 the area of the original triangle. The question is can angle bisectors of a triangle form a triangle. I do understand that if we are talking about equilateral triangle, they will because angle bisectors, medians and altitudes are one and the same. What about a scalene triangle, and an iscosecles one.
Medians - I tried using vectors to prove the same. I took the three points and then mid points. Using position vectors, I came up with three vectors whose addition is equal to zero, so I said they will form a triangle. The same thing is not working with angle bisectors.