Question 82
Given a quadrilateral $ABCD$ set $AB = a$, $BC = b$, $CD = c$, $DA = d$, $AC = e$ and $BD = f$. Prove that:
a) $a^{2} + b^{2} + c^{2} + d^{2} \geq e^{2} + f^{2}$;
b) if the quadrilateral $ABCD$ is cyclic then $|a - c| \geq |e - f|$.
a) $a^{2} + b^{2} + c^{2} + d^{2} \geq e^{2} + f^{2}$;
b) if the quadrilateral $ABCD$ is cyclic then $|a - c| \geq |e - f|$.