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2014 preRMO p10, computational with ratios and areas

Source:

August 9, 2019
ratiogeometryareas

Problem Statement

In a triangle ABC,XABC, X and YY are points on the segments ABAB and ACAC, respectively, such that AX:XB=1:2AX : XB = 1 : 2 and AY:YC=2:1AY :YC = 2:1. If the area of triangle AXYAXY is 1010, then what is the area of triangle ABCABC?
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