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Let f, g and h be the lengths of the per...

Let `f, g and h` be the lengths of the perpendiculars from the circumcenter of `Delta ABC` on the sides a, b, and c, respectively. Prove that `(a)/(f) + (b)/(g) + (c)/(h) = (1)/(4) (abc)/(fgh)`

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To prove the equation \[ \frac{a}{f} + \frac{b}{g} + \frac{c}{h} = \frac{1}{4} \cdot \frac{abc}{fgh} \] where \(f\), \(g\), and \(h\) are the lengths of the perpendiculars from the circumcenter \(O\) of triangle \(ABC\) to the sides \(BC\), \(CA\), and \(AB\) respectively, we will follow these steps: ...
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