The quadrilateral $ABCD$, in which $\angle BAC < \angle DCB$ , is inscribed in a circle $c$, with center $O$. If $\angle BOD = \angle ADC = \alpha$. Find out which values of $\alpha$ the inequality $AB <AD + CD$ occurs.
Problem
Source: 2016 Bulgaria JBMO TST 1.1
Tags: geometry, geometric inequality, angles, cyclic quadrilateral