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!

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## Comments

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TopNewestWhat does 'thers is a circle of ABC' mean? Does that mean that the circle is an incircle?

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So stupid of me, Mr.Wen, I actually meant "triangle".

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Hey do you know complex bash?? If yes then try it on this problem. Take the incircle as the unit circle. And take A,B,C as functions of D,E,F then find the coordinates of M and N and use the collinearity condition.

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