Problem Let $\text{ABC}$ be a triangle and let $\text{I}$ , $\text{J}$ and $\text{K}$ be points such that: $\vec{\text{BI}}=\frac{1}{2}\vec{\text{IC}}$, $\vec{\text{AJ}}=2\vec{\text{JB}}$ and $\vec{\text{AK}}=\frac{1}{3}\vec{\text{AC}}$. Let $\text{E}$ be the centre of $\text{[BC...

Problem Let $\text{ABC}$ be a triangle, and $\text{M}$ and $\text{N}$ are points where: $\vec{\text{AM}}=\frac{1}{3}\vec{\text{AB}}$ and $\vec{\text{AN}}=\frac{1}{2}\vec{\text{AB}}$ and $\text{M'}$ and $\text{N'}$ are points in $\text{[AC]}$ such that both $\text{(NN')}$ and $\text{(MM')}...