Collinear points...

Let $\omega,I,I_A$ be the incircle, incenter, excenter of $\triangle ABC$ respectively. Let $D,E,F$ be the tangency points of the incircle with sides $BC,CA,AB$ respectively. Let $\Gamma$ be the circumcircle of $\triangle IBC$ . Let $M$ and $N$ be the intersections of $\Gamma$ and $\omega$ with $M$ nearer to $B$ . Let $BI_A$ and $FM$ meet at $X$ . Prove that $N,D,X$ are collinear.

#Geometry

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$