Let $ABC$ be an equilateral triangle with side length $8$, and let $D$, $E$, and $F$ be points on the sides $BC$, $CA$, and $AB$ respectively. Given that $BD = 2$ and $\angle ADE = \angle DEF = 60^\circ$, calculate the length of segment $AF$.
Problem
Source: 2024 Argentina L2 P1
Tags: geometry
LiamChen
19.11.2024 10:27
By using law of cosine in triangle AEF we get AF=sqrt(58).
BR1F1SZ
19.11.2024 22:45
LiamChen wrote: By using law of cosine in triangle AEF we get AF=sqrt(58). That's not the right answer... Hint: Find similar triangles
offidy
20.11.2024 22:29
Erm if you know and understand the answer already why are you still posting this?
BR1F1SZ
20.11.2024 23:07
offidy wrote: Erm if you know and understand the answer already why are you still posting this? For other people to discuss it and share different solutions! It's the whole point of AoPS! Also, I wanted to keep the contest collection updated.