frac{1}{r^2}+frac{1}{r_1^2}+frac{1}{r_2^2}+fr | vedclass

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(B) We know that $r = \frac{\Delta}{s}$,$r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c}$.Substituting these values

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$\frac{a^2+b^2+c^2}{\Delta^2}$

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(B) We know that $r = \frac{\Delta}{s}$,$r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c}$.Substituting these values into the expression:$\frac{1}{r^2} + \frac{1}{r_1^2} + \frac{1}{r_2^2} + \frac{1}{r_3^2} = \frac{s^2}{\Delta^2} + \frac{(s-a)^2}{\Delta^2} + \frac{(s-b)^2}{\Delta^2} + \frac{(s-c)^2}{\Delta^2}$$= \frac{s^2 + (s-a)^2 + (s-b)^2 + (s-c)^2}{\Delta^2}$$= \frac{s^2 + (s^2 - 2as + a^2) + (s^2 - 2bs + b^2) + (s^2 - 2cs + c^2)}{\Delta^2}$$= \frac{4s^2 - 2s(a+b+c) + a^2+b^2+c^2}{\Delta^2}$Since $a+b+c = 2s$,we have:$= \frac{4s^2 - 2s(2s) + a^2+b^2+c^2}{\Delta^2}$$= \frac{4s^2 - 4s^2 + a^2+b^2+c^2}{\Delta^2}$$= \frac{a^2+b^2+c^2}{\Delta^2}$

$\frac{1}{r^2}+\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}$ equals

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