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!

## Comments

Sort by:

TopNewestWhat does 'thers is a circle of ABC' mean? Does that mean that the circle is an incircle? – Wen Z · 8 months ago

Log in to reply

– S M · 7 months ago

So stupid of me, Mr.Wen, I actually meant "triangle".Log in to reply

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. – Racchit Jain · 6 months ago

Log in to reply