If In`(a+c),ln(a-c),ln(a-2b+c)` are in `AdotPdot,` then `a , b , c ,a r einAdotPdot` (b) `a^2,b^2,c^2a r einAdotPdot` `a , b , c` are in `GdotPdot` (d) `a , b , c` are in `HdotPdot`

If log(a+c)+log(a+c-2b)=2log(a-c) then

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot

If in a A B C ,(sinA)/(sinC)=(sin(A-B))/(sin(B-C) , prove that a^2,b^2,c^2 are in AdotPdot

Column I, Column II If a ,b ,c ,a n dd are four zero real numbers such that (d+a-b)^2+(d+b-c)^2=0 and he root of the equation a(b-c)x^2+b(c-a)x=c(a-b)=0 are real and equal, then, p. a+b+c=0 If the roots the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal, then, q. a ,b ,ca r einAdotPdot If the equation a x^2+b x+c=0a n dx^3-3x^2+3x-0 have a common real root, then, r. a ,b ,ca r einGdotPdot Let a ,b ,c be positive real number such that the expression b x^2+(sqrt((a+b)^2+b^2))x+(a+c) is non-negative AAx in R , then, s. a ,b ,ca r einHdotPdot

If a ,\ b ,\ c are in proportion, then (a) a^2=b c (b) b^2=a c (c) c^2=a b (d) None of these

In a triangle ABC, if sinAsin(B-C)=sinCsin(A-B), then prove that cotA ,cotB ,cotCa r einAdotPdot

If A,B,C, are the angles of a triangle such that cot(A/2)=3tan(C/2), then sinA ,sinB ,sinC are in (a) AdotPdot (b) GdotPdot (c) HdotPdot (d) none of these

a, b, c are sides of a triangle and a, b, c are in GP If log a- log 2b, log 2b-log 3c and log 3c-log a are in AP then

a, b, c are sides of a triangle and a, b, c are in GP If log a- log 2b, log 2b-log 3c and log 3c-log a are in AP then

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-a^2b-a b^2,and C=a^2c +'a c^2-b^2' c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot