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If in a triangle ABC r1= 6 r2=3 r3= 2 then find the area of triangle.also find out a+b+c

If in a triangle ABC r1= 6 r2=3 r3= 2 then find the area of triangle.also find out a+b+c

Grade:11

1 Answers

mycroft holmes
272 Points
4 years ago
We use the formulae:
r = \frac{\Delta}{s}; r_1 = \frac{\Delta}{s-a}; r_2 = \frac{\Delta}{s-b}; r_3 = \frac{\Delta}{s-c}
 
We can then easily prove that 
 
\frac{1}{r} = \frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}
 
and hence we get r = 1. 
 
Further we have rr_1r_2r_3 = \frac{\Delta}{s} \frac{\Delta}{s-a}\frac{\Delta}{s-b} \frac{\Delta}{s-c}
 
= \frac{\Delta^4}{s(s-a)(s-b)(s-c)} = \frac{\Delta^4}{\Delta^2} = \Delta^2
 
Which means \Delta^2 = 36 \implies \Delta=6
 
Then we easily get s = 6 and hence a+b+c = 12

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