MathDB

3

Part of 1999 Poland - Second Round

Problems(1)

ratio of triangle area indepedent of choices of 2 points, ratios in cyclic

Source: Polish second round 1999 p3

1/19/2020
Let ABCDABCD be a cyclic quadrilateral and let EE and FF be the points on the sides ABAB and CDCD respectively such that AE:EB=CF:FDAE : EB = CF : FD. Point PP on the segment EF satsfies EP:PF=AB:CDEP : PF = AB : CD. Prove that the ratio of the areas of △APD\vartriangle APD and △BPC\vartriangle BPC does not depend on the choice of EE and FF.
ratiogeometrycyclic quadrilateralarea of a triangleareas