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

Question

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

SHAIK AASIF AHAMED · Answer

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

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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

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

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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

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

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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