Question
If the exradii of a triangle are in H.P. then the corresponding sides are in
A.
A.P.
B.
G.P.
C.
H.P.
D.
None of these
Answer :
A.P.
Solution :
$$\eqalign{
& \frac{1}{{{r_1}}},\frac{1}{{{r_2}}},\frac{1}{{{r_3}}}\,{\text{are in A}}{\text{.P}}{\text{.}} \cr
& \Rightarrow \,\,\frac{{s - a}}{\vartriangle },\frac{{s - b}}{\vartriangle },\frac{{s - c}}{\vartriangle }\,{\text{are in A}}{\text{.P}}{\text{.}} \cr
& \Rightarrow \,\,s - a,s - b,s - c\,{\text{are in A}}{\text{.P}}{\text{.}} \cr
& \Rightarrow \,\, - a, - b, - c\,{\text{are in A}}{\text{.P}}{\text{.}} \cr} $$