# 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.

# First look at the knowledge graph.

# Next understand the problem

In triangle 𝐴𝐵𝐶, point 𝐷 divides side AC so that 𝐴𝐷 ∶ 𝐷𝐶 = 1 ∶ 2. Let 𝐸 be the midpoint of BD and 𝐹 be the point of intersection of line BC and line AE. Given that the area of ∆𝐴𝐵𝐶 is 360, what is the area of ∆𝐸𝐵𝐹?

##### Source of the problem

American Mathematical Contest 2019, AMC 8 Problem 25

##### Key Competency

Menalaus’s Theorem:

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 Mathematics

# Watch video

# 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.