MathNet 2003 — Part 01 Question 86

The incircle of $\triangle ABC$ has radius $r$ and is tangent to the sides $AB$, $BC$ and $CA$ at points $C_1$, $A_1$ and $B_1$, respectively. If $N = BC \cap B_1C_1$ and $AA_1 = 2A_1N = 2r\sqrt{3}$, find $\measuredangle ANC$.