Triangle ABC has altitudes

h_{1}

h_{2}

and

h_{3}

The radius of the inscribed circle is $r$ , while the radii of the escribed circles are $r_{1}$ , $r_{2}$ and $r_{3}$ respectively. "

Prove:

$\frac{1}{r} = \frac{1}{h_{1}} + \frac{1}{h_{2}} + \frac{1}{h_{3}} = \frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} .$ $(1)$