Let a,b, and c are the lengths of the sides of $\displaystyle \triangle ABC $,and x,y,z be the lengths of the perpendiculars drawn from the circumcentre onto the sides BC,CA and AB respectively. prove that

$\displaystyle \frac{a}{x}+\frac{b}{y}+\frac {c}{z} = \frac{abc}{4xyz} $

(Thinking)