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S (ABC): S (ADC) wanted, cyclic BACD, AC =56, BD = 65, BC>DA, AB: BC =CD:DA

Source: December 2020 Ukraine Geometry Olympiad IX p2 , X p1 , XI p1

December 20, 2020
geometryareasratio

Problem Statement

Let ABCDABCD be a cyclic quadrilateral such that AC=56,BD=65,BC>DAAC =56, BD = 65, BC>DA and AB:BC=CD:DAAB: BC =CD: DA. Find the ratio of areas S(ABC):S(ADC)S (ABC): S (ADC).
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