SAT1000 - P844

Geometry Level pending

As shown above, $F(1,0)$ is the focus of the parabola $C: y^2=4x$ , line $l: y=k(x-1)$ intersects with $C$ at point $A,B$ , and the perpendicular bisector of $AB$ intersects with $C$ at point $M,N$ .

If $A,M,B,N$ are on the same circle, then find the value of $\lfloor 1000|k| \rfloor$ .

Have a look at my problem set: SAT 1000 problems