posted by Anonymous .
ABC is a triangle with ∠BAC=60∘,AB=5 and AC=25. D is a point on the internal angle bisector of ∠BAC such that BD=DC. What is AD^2?
using the law of cosines, if we let AD=x,
x^2 + 5^2 - 2x(5)cos30 = x^2 + 25^2 - 2x(25)cos30
25-5x√3 = 625-25x√3
20x√3 = 600
x = 30/√3
x^2 = 300