Question 17
Trapezoid $ABCD$ is inscribed in the parabola $y = x^{2}$ such that $A = (a, a^{2})$, $B = (b, b^{2})$, $C = (-b, b^{2})$, and $D = (-a, a^{2})$ for some positive reals $a, b$ with $a \gt b$. If $AD + BC = AB + CD$, and $AB = \frac{3}{4}$, what is $a$?
