Question 9
In triangle ABC, the internal bisector of $$\angle{A}$$ meets BC at D. If AB = 4, AC = 3 and $$\angle{A}$$ = 60° , then the length of AD is
Solution
By using cosine rule we can find BC = $$\sqrt{13}$$ . By angle bisector theorem we have BA / BD = AC / DC . Also BD + DC = $$\sqrt{13}$$. So by substitution we get we get BD = 4*$$\sqrt{13}$$/7 . Now using cosine rule in triangle ABD taking AD = x, we get
$$x^2 - 4*\sqrt13*x + 16*(36/49) = 0$$. Solving the equation we get x = $$\frac{12\sqrt 3}{7}$$ .
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