Question 101·200 Super-Hard SAT Math Questions·Geometry and Trigonometry

Type the circle equation and $y=2x-1$ on separate Desmos lines. Click both crossings. Desmos shows approximately $(-2.59,-6.18)$ and $(1.39,1.78)$. Those crossings are the chord’s endpoints, so the distance between them is the length you need.

Type $A=(-2.59,-6.18)$ and $B=(1.39,1.78)$. Desmos plots them close to the crossings. These are rounded coordinates, not exact values, so use them to estimate the length rather than to claim an exact radical.

Type $\operatorname{distance}(A,B)$. Desmos prints about $8.89955$. The distance formula includes both the horizontal and vertical changes, so this is the straight-line length, not just the change in $x$.

Enter the four choices on new Desmos lines. They evaluate to about $3.98$, $4.45$, $8.90$, and $44.50$, in that order. The third value matches the measured length. Don’t halve it: $A$ and $B$ already mark opposite ends of the chord. The distance between the intersection points is $\frac{6\sqrt{55}}{5}$. Choice C.