# (Color+beauti)ful Hexagon!

**Geometry**Level 3

**regular**hexagon \(ABCDEF\), the segments \(BD, BE, CA\) are drawn.

\(BD\) and \(CA\) intersect at point \(Q\).

\(BE\) and \(CA\) intersect at point \(P\).

\(A(\triangle BPQ)\) is colored \(\color{Green}{\text{green}}\)

\(A(\triangle BCD)\) is colored \(\color{Red}{\text{red}}\)

Rest of the area is colored \(\color{Purple}{\text{purple}}\)

If the ratio of areas of colors

\(\color{Purple}{\text{purple}}:\color{Green}{\text{green}}:\color{Red}{\text{red}}=\color{Purple}{a}:\color{Green}{b}:\color{Red}{c}\)

such that \(a,b,c \in \mathbb{N}\) , \(\text{gcd}(a,b,c)=1\).

Find \(a+b+c\)

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.