MathNet 2021 — Part 10 Question 77

Question 77

In quadrilateral $ABCD$, $\angle CBA = 90^\circ$, $\angle BAD = 45^\circ$, and $\angle ADC = 105^\circ$. Suppose that $BC = 1 + \sqrt{2}$ and $AD = 2 + \sqrt{6}$. What is the length of $AB$?

$2\sqrt3$
$2+\sqrt3$
$3+\sqrt2$
$3+\sqrt3$