Let $ABCD$ be a cyclic quadrilateral such that $AC =56, BD = 65, BC>DA$ and $AB: BC =CD: DA$. Find the ratio of areas $S (ABC): S (ADC)$.
Problem
Source: December 2020 Ukraine Geometry Olympiad IX p2 , X p1 , XI p1
Tags: geometry, areas, ratio
Source: December 2020 Ukraine Geometry Olympiad IX p2 , X p1 , XI p1
Tags: geometry, areas, ratio
Let $ABCD$ be a cyclic quadrilateral such that $AC =56, BD = 65, BC>DA$ and $AB: BC =CD: DA$. Find the ratio of areas $S (ABC): S (ADC)$.