There is a triangle of \(ABC\) that has center \(I\) and touches the side \(BC\) at \(D\). Let the midpoints of \(AD\) and \(BC\) be \(M\) and \(N\), respectively. Prove that \(M,I,N\) are colllinear.
So I am in class 11, CBSE, India, I consider myself average in Mathematics. I recently got selected for an Olympiad, and then this question pops up in my favorite area of Math and it borderline depresses me that I can't solve it, please help!