Problem (2011ARMOg11p8): Let $N$ be the midpoint of arc $ABC$ of the circumcircle of triangle $ABC$, let $M$ be the midpoint of $AC$ and let $I_1, I_2$ be the incentres of triangles $ABM$ and $CBM$. Prove that points $I_1, I_2, B, N$ lie on a circle.
AlphaGeometry formalization: a b c = triangle; o = circumcenter a b c; n = on_circle o a, on_bline a c; m = midpoint a c; i1 = incenter a b m; i2 = incenter c b m ? cyclic i1 i2 b n
HAGeo formalization: A B C = triangle; O = circumcenter A B C; N = midarc A B C; M = midpoint A C; I1 = incenter A B M; I2 = incenter C B M; Prove: concyclic I1 I2 B N
Difficulty score: 3.0