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in a trainagle,R & r are the circumradius and inradius respectively then the H.M of the exradius the triangle is ???????????
Dear Zyesha,
let r1 , r2 , r3 be the three exradii
r1= Δ/(s-a) ,r2= Δ/(s-b) , r3= Δ/(s-c)---------------1
where Δ is the area of triangle and s = (a+b+c)/2
the harmonic means of the three exradii are
H.M = 3/(1/r1 + 1/r2 + 1/r3) ---------------2
putting the value of r1,r2,r3 from 1 to 2
H.M= 3Δ/(s-a+s-b+s-c)
so H.M = 3Δ/s
and we know that
r = Δ/s
so H.M of exradii = 3 r
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