# Altered from Another Problem

Geometry Level 3

Let $$ABC$$ be a scalene triangle and $$M$$ be the midpoint of $$BC$$. The incircle centered at $$I$$ touches $$BC$$ at $$D$$. Denote by $$N$$ the midpoint of $$AD$$.

Transpose the figure to the complex plane and find $$(N-I)(\overline{M} - \overline{I}) - (\overline{N} - \overline{I})(M-I)$$ , where N, M, I denote the complex numbers of their respective points.

×