Question 22
In $\triangle ABC$ below, $\angle A=60^\circ$ and the lengths AB and AC are roots of $x^2-5x+3=0$. D lies on BC and AD bisects $\angle A$. AB and AC are tangent to a circle with centre D. Its radius is $a\sqrt b/c$, where a and c have no common factor and b has no square factor. Find $a+b+c$.
