in triangle ABC PROVE THAT 1/r1+1/r2+1/r3=1/r

Question

SIR I AM SOUMYA SEN

HELP  ME PLZZZZZZZZZZZZZ

Answer 1

To Prove : 1/r1+1/r2+1/r3=1/r 

LHS =>  1/(Δ/s-a) + 1/(Δ/s-b) + 1/(Δ/s-c)

    = s-a/Δ + s-b/Δ + s-c/Δ

 = (s-a+s-b+s-c)/Δ

= {3s+ - (a+b+c)}/Δ

= [3s - 2s]/Δ

= s/Δ    { r = Δ/s }

So s/Δ = 1/(Δ/s) = 1/r

LHS = RHS

Proved

- (Devansh Gaur) 

www.facebook.com/DevanshGaurOfficial

Answer 2

(question from properties of triangle)

the value of (r1​-r) (r2+r3) =

Answer 3

we know that r= Δ/s,r1=Δ/(s-a),r2=Δ/(s-b),r3=Δ/(s-c)

from above put the value of respective in L.H.S.

then it becomes

=(s-a)/Δ + (s-b)/Δ + (s-c)/Δ

=(s-a)+(s-b)+(s-c)/Δ

= 3s-a-b-c/Δ

=3s-(a+b+c)/Δ

=3s-2s/Δ      ( we know that s=a+b+c/2)

= s/Δ

=1/(Δ/s)

= 1/r

= R.H.S proved.

( ashok.khatri.9@facebook.com)