2018 AIME I Problems/Problem 8
Let 
be an equiangular hexagon such that 
, and 
. Denote 
the diameter of the largest circle that fits inside the hexagon. Find 
.
Solutions
Solution Diagram
- cooljoseph
First of all, draw a good diagram! This is always the key to solving any geometry problem. Once you draw it, realize that 
. Why? Because since the hexagon is equiangular, we can put an equilateral triangle around it, with side length 
. Then, if you drew it to scale, notice that the "widest" this circle can be according to 
is 
. And it will be obvious that the sides won't be inside the circle, so our answer is 
.
-expiLnCalc
