## AIME II 2018 problem 4

For discussing Olympiad level Geometry Problems
samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### AIME II 2018 problem 4

In equiangular octagon $CAROLINE$, $CA = RO = LI = NE =$ $\sqrt{2}$ and $AR = OL = IN = EC = 1$. The self-intersecting octagon $CORNELIA$ encloses six non-overlapping triangular regions. Let $K$ be the area enclosed by $CORNELIA$, that is, the total area of the six triangular regions. Then $K =$ $\dfrac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Find $a + b$.

Ragib Farhat Hasan
Posts: 62
Joined: Sun Mar 30, 2014 10:40 pm

### Re: AIME II 2018 problem 4

After the tedious calculations, I found the answers to be $a=25$ and $b=6$.
Therefore, $a+b=31$.

But I'm too tired to write the full solution right now. Hopefully, I will post it when I feel like!

Till then, I invite someone else to prove my answer. Good luck!