ΔABC is a right triangle with BAC as the right angle and AB = 3, AC = 6. AD is the bisector of BAC. What is the length of AD?
answer is 2√3
procedure: as AD is the angle bisector then it is the property of angle bisector that AB/AC = BD/DC it can also be proved then let BD = x and correspondingly DC= 3√3 - x so you will get x and also calculate angle A by cosine rule you will get A = 60 deg then A/2 = 30 deg then again applies cosine rule in triangle ABD you will get AD = 2√3
cosine rule is in triangle ABC , cosA = [(AB)^2 + (AC)^2 - (BC)^2]/2*AB*AC