Is the language $\{a^n b^n c^i | i \leq n\}$ context free?
Classical pumping works. According to the pumping lemma we can find a segmentation $uvwxy$ such that $uv^iwx^iy$ is in the language for all $i$.

Start with your own suggestion $a^pb^pc^p $.

Three easy steps.


Each of the "pumping segments" $v$, $x$ can only be within the boundaries of one the "letter segments" $a^p$, $b^p$, $c^p$. 
It is not possible to have one of $v$ or $x$ to be in the $a^p$ segment without the other being inside the $b^p$ segment. And the other way around. In that case pump down ($i=0$).
Final possibility both $v$ and $x$ are in $c^p$. Pump up.