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ratio of areas within an equilateral triangle

Source: May Olympiad (Olimpiada de Mayo) 1998 L2

September 12, 2018
geometryareasEquilateral Triangle

Problem Statement

Let ABCABC be an equilateral triangle. NN is a point on the side ACAC such that AC⃗=7AN⃗\vec{AC} = 7\vec{AN}, MM is a point on the side ABAB such that MNMN is parallel to BCBC and PP is a point on the side BCBC such that MPMP is parallel to ACAC. Find the ratio of areas (MNP)(ABC)\frac{ (MNP)}{(ABC)}
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