MathDB
Many Many Intersections

Source: Mexico

February 7, 2022
geometryparallelogramcircumcircle

Problem Statement

Let ABCDABCD be a parallelogram (non-rectangle) and Γ\Gamma is the circumcircle of △ABD\triangle ABD. The points EE and FF are the intersections of the lines BCBC and DCDC with Γ\Gamma respectively. Define P=ED∩BAP=ED\cap BA, Q=FB∩DAQ=FB\cap DA and R=PQ∩CAR=PQ\cap CA. Prove that PRRQ=(BCCD)2\frac{PR}{RQ}=(\frac{BC}{CD})^2
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