in triangle ABC prove that 1/r1+1/rr2/1/r3=1/r

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1 Answer

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)+(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.

 

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