Mathematics - Properties of Triangle Question with Solution | TestHub

In a $△ABC$, perpendiculars are drawn from the angles $A,B,C$ of an acute angled triangle on the opposite sides and produced to meet the circumscribing circle at $D,E$ and $F$ respectively. If these produced parts be $\alpha ,\beta ,\gamma$ respectively. Then the value of $\frac{\left(\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }\right)}{\tan A+\tan B+\tan C}$ is