MathNet 2006 — Part 04 Question 28

In a cyclic quadrilateral $ABCD$, $AB = a$, $BC = b$, $CD = c$, $\angle ABC = 120^\circ$, and $\angle ABD = 30^\circ$. Prove that

i) $c \geq a + b$;

ii) $|\sqrt{c+a} - \sqrt{c+b}| = \sqrt{c-a-b}$.