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Competency in Focus: Menalaus’s Theorem This problem from American Mathematics contest (AMC 8, 2019) will help us to learn more about Menalaus’s Theorem.ย 

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In triangle ๐ด๐ต๐ถ, point ๐ท divides side AC so that ๐ด๐ท โˆถ ๐ท๐ถ = 1 โˆถ 2. Let ๐ธ be the midpoint of BD and ๐น be the point of intersection of line BC and line AE. Given that the area of โˆ†๐ด๐ต๐ถ is 360, what is the area of โˆ†๐ธ๐ต๐น?
Source of the problem
American Mathematical Contest 2019, AMC 8 Problem 25

Key Competency
Menalaus’s Theorem:ย ย  Given a triangle ABC, and a transversal line that crosses BC, AC, and AB at points D, E, and F respectively, with D, E, and F distinct from A, B, and C, then

$$ \displaystyle {\frac {AF}{FB}\times \frac {BD}{DC}\times \frac {CE}{EA}=-1.}$$

Difficulty Level


Suggested Book
Challenges and Thrills in Pre College Mathematics Excursion Of Mathematicsย 

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