The diagonals $AC$ and $BD$ of the cyclic quadrilateral $ABCD$ intersect at a point O. It is known that $\angle BAD = 60^o$ and $AO = 3OC$. Prove that the sum of some two sides of a quadrilateral is equal to the sum of the other two sides.
Problem
Source: 2012 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p10
Tags: geometry, equal segments, cyclic quadrilateral, Ukraine Correspondence