SEAMO 2022 — Paper D — Grade 7–8 Question 22

Triangle ABC has angle A sixty degrees, AB and AC the roots of $x^2-5x+3=0$. The angle bisector meets BC at D. A circle centered at D is tangent to AB,AC; its radius is $a\sqrt b/c$, with a,c coprime and b squarefree. Find a+b+c.