If r_1, r_2, r_3 are the radii of the excircl | vedclass

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(C) We know that the radii of the excircles are given by $r_1 = s 	an \frac{A}{2}$,$r_2 = s 	an \frac{B}{2}$,and $r_3 = s 	an \frac{C}{2}$.Sum of r

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$\sum 	an \frac{A}{2}$

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(C) We know that the radii of the excircles are given by $r_1 = s 	an \frac{A}{2}$,$r_2 = s 	an \frac{B}{2}$,and $r_3 = s 	an \frac{C}{2}$.Sum of radii: $\sum r_1 = s(	an \frac{A}{2} + 	an \frac{B}{2} + 	an \frac{C}{2})$.Also,$\sum r_1 r_2 = s^2(	an \frac{A}{2} 	an \frac{B}{2} + 	an \frac{B}{2} 	an \frac{C}{2} + 	an \frac{C}{2} 	an \frac{A}{2})$.Using the identity $\sum 	an \frac{A}{2} 	an \frac{B}{2} = 1$ for any triangle $ABC$,we have $\sum r_1 r_2 = s^2(1) = s^2$.Therefore,$\frac{\sum r_1}{\sqrt{\sum r_1 r_2}} = \frac{s \sum 	an \frac{A}{2}}{\sqrt{s^2}} = \sum 	an \frac{A}{2}$.

If $r_1, r_2, r_3$ are the radii of the excircles of triangle $ABC$,then $\frac{\sum r_1}{\sqrt{\sum r_1 r_2}}$ is equal to:

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