SAT1000 - P808

Geometry Level pending

As shown above, the ellipse has equation: $\dfrac{x^2}{4}+y^2=1$ .

If line $l$ passes through point $C(m,0)$ and is tangent to circle: $x^2+y^2=1$ .

$l$ intersects with the ellipse at point $A,B$ , then find the maximum value of $|AB|$ .

Let $M$ be the maximum value. Submit $\lfloor 1000M \rfloor$ .

Have a look at my problem set: SAT 1000 problems