Problem source

{\it Note that the volume of a 
tetrahedron is equal to  $\frac1  3$ $\times$ 
the area of the base $\times$ the height.}
The points $O$, $A$, $B$ and $C$ have coordinates $(0,0,0)$, $(a,0,0)$, $(0,b,0)$
and $(0,0,c)$, respectively, where $a$, $b$ and $c$ are positive.
\begin{questionparts}
\item Find, in terms of $a$, $b$ and $c$,  the volume of the tetrahedron
  $OABC$.
\item
 Let angle $ACB = \theta$. Show that
\[
\cos\theta = 
\frac {c^2}
{ 
{ \sqrt{\vphantom{ \dot b}
(a^2+c^2)(b^2+c^2)} }
^{\vphantom A}    
\  }
\]
and find, in terms of $a$, $b$ and $c$, the  area of triangle $ABC$.
% is 
%$\displaystyle \tfrac12 \sqrt{ \vphantom{\dot A } a^2b^2 +b^2c^2 + c^2 a^2 \;} \;$.
\end{questionparts}
Hence show that $d$,  the perpendicular distance of the origin from
the  triangle $ABC$, satisfies
\[
\frac 1{d^2} = \frac 1 {a^2} + \frac 1 {b^2} + \frac 1 {c^2} \,.
\]