Tryin' to help my niece on her homework: The area of triangle ABC is 133. The angle bisectors meet at point I. AB:BC:CA=4:7:8. What is the area of triangle BCI?
We have that angle bisectors meet at the circumcenter, which is the center of the circumscribed circle. We have a bunch of things about medians, perpendicular bisectors, and altitudes. It seems logical that BCI is about 1/3 of ABC, but you know the math teacher isn't going to accept that for an answer.