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ratio of areas (APM)/(ABCD), trapezoid ABCD, AB/CD=3/2, BN = 3NC, AM = 2MB

Source: 2022 Chile National Olympiad level 1 p2

October 22, 2022
ratiogeometrytrapezoidareas

Problem Statement

In a trapezoid ABCDABCD whose parallel sides ABAB and CDCD are in ratio ABCD=32\frac{AB}{CD}=\frac32, the points N N and MM are marked on the sides BCBC and ABAB respectively, in such a way that BN=3NCBN = 3NC and AM=2MBAM = 2MB and segments ANAN and DMDM are drawn that intersect at point PP, find the ratio between the areas of triangle APMAPM and trapezoid ABCDABCD. https://cdn.artofproblemsolving.com/attachments/7/8/21d59ca995d638dfcb76f9508e439fd93a5468.png
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