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Grade Upto college level Algebra

If ex-radii r1, r2, r3 of a triangle ABC are in H.P., then the sides of the triangle are in A. A.P. B. G.P. C. H.P. D. none of the above

Profile image of Manvendra Singh chahar
12 Years agoGrade Upto college level
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1 Answer

Profile image of SHAIK AASIF AHAMED
12 Years ago
Using the relations
r1 = S/(s-a) where S = area and s is semi-perimeter.
r2 = S/(s-b)
r3 = S/(s-c).
As the radii are in HP their reciprocals are in A.P.
So (s-a)/S,..,.. are in AP or s-a, s-b, s-c are in AP so a,b,c are in AP
Hence A is the correct answer
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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