If `a,b,c` are in AP, then show that `r_(1), r_(2), r_(3)` are in HP.

If in Delta ABC, (a -b) (s-c) = (b -c) (s-a) , prove that r_(1), r_(2), r_(3) are in A.P.

In a DeltaABC, show that r_(1)* r_(2)* r_(3)*r=Delta^(2).

In a triangle ABC if sides a = 13, b =14 and c = 15, then reciprocals of r_(1),r_(2),r_(3) are in the ratio

Assertion: a^2,b^2,c^2 are in A.P., Reason: 1/(b+c), 1/(c+a), 1/(a+b) are in A.P. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Show that r_(1)+r_(2)=c cot ((C)/(2))

If the numbers p,q,r are in A.P. then m^(7p), m^(7q), m^(7r)(mgt0) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Statement I In a Delta ABC, if a lt b lt c and r is inradius and r_(1) , r_(2) , r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

The circuit is shown in the following figure. The potential at points A, B, C, D and O are given. The currents in the resistance R_(1), R_(2) and R_(3) are in the ratio of 4:2:1 . What is the ratio of resistance R_(1),R_(2),R_(3) and R_(4) ?

Show that 16R^(2)r r_(1) r _(2) r_(3)=a^(2) b ^(2) c ^(2)

Prove that r_(1)^(2)+r_(2)^(2) +r_(3)^(3) +r^(2) =16R^(2) -a^(2) -b^(2) -c^(2). where r= in radius, R = circumradius,, r_(1), r_(2), r_(3) are ex-radii.