Categories

# 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

# Next understand the problem

In triangle ๐ด๐ต๐ถ, point ๐ท divides side AC so that ๐ด๐ท โถ ๐ท๐ถ = 1 โถ 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 โ๐ด๐ต๐ถ is 360, what is the area of โ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

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

7/10

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

# Connected Program at Cheenta

#### Amc 8 Master class

Cheenta AMC Training Camp consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams.