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In a triangle abc, r1r2+r2r3+r3r1 is equal to( where r1, r2, r3 are the exradii and 2s is the perimeter)

In a triangle abc,  r1r2+r2r3+r3r1 is equal to( where r1, r2, r3 are the exradii and 2s is the perimeter) 
 
 

Grade:11

1 Answers

Vikas TU
14149 Points
one year ago
 
Dear student 
r1r2 +r2r3+ r3r1  =??
Δ/(s-a) * Δ/(s-b) + Δ/(s-b) * (s-c) + Δ/(s-c)*(s-a)
Δ2 ( 1/(s-a)(s-b) + 1/(s-b)(s-c) + 1/(s-c)(s-a) )
Δ2 ( 3s- (a+b+c)/(s-a)(s-b)(s-c))
Put value of s = (a+b+c)/2
So it will be equal to s2

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