# JOMO 5, Short 10

**Geometry**Level 5

The product of \(OG, BG, BI, IE, OE, GE, GK, KE\) and \(IK\) can be expressed as \(\frac{a\sqrt b}c\) where \(a,b,c\in \mathbb Z^+\), \(gcd(a,c)=1\), and \(b\) is not divisible by the square of a integer larger than 1. Find the last 3 digits of \(a+b+c\)