The median in a isosceles triangle is ortoghonal into a hilbert space

Question

how can I prove that if $p$, $q$, $r$ and $o$ are points in a Hilbert space such that $p$, $q$, $o$ are collinear, $\|p-o\|=\|q-o\|$ and $\|p-r\|=\|q-r\|$ then $r-o \perp p-o$?.

I think it's a simple count but I can't do, can anybody help me?