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
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