What are we learning ?
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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Next understand the problem
In triangle ๐ด๐ต๐ถ, point ๐ท divides side AC so that ๐ด๐ท โถ ๐ท๐ถ = 1 โถ 2. Let ๐ธ be the midpoint of BD and ๐น be the point of intersection of line BC and line AE. Given that the area of โ๐ด๐ต๐ถ is 360, what is the area of โ๐ธ๐ต๐น?
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
7/10
Suggested Book
Challenges and Thrills in Pre College Mathematics Excursion Of Mathematicsย
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