2016 AMC 12A Problems/Problem 12
In , , , and . Point lies on , and bisects . Point lies on , and bisects . The bisectors intersect at . What is the ratio : ?
By the angle bisector theorem,
Now, we use mass points. Assign point a mass of .
Similarly, will have a mass of
Denote as the area of triangle ABC and let be the inradius. Also, as above, use the angle bisector theorem to find that . Note that is the incenter. Then,