In Delta ABC,if a, b, c are in A.P. (with usu | vedclass

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(C) Given $a, b, c$ are in $A.P.$By the sine rule,$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R$.Thus,$\sin A, \sin B, \sin C$ are prop

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$r_1, r_2, r_3$ are in $A.P.$

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(C) Given $a, b, c$ are in $A.P.$By the sine rule,$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R$.Thus,$\sin A, \sin B, \sin C$ are proportional to $a, b, c$,so they are in $A.P.$Altitudes $h_1, h_2, h_3$ are given by $h_1 = \frac{2 \Delta}{a}, h_2 = \frac{2 \Delta}{b}, h_3 = \frac{2 \Delta}{c}$. Since $a, b, c$ are in $A.P.$,their reciprocals $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in $H.P.$,so $h_1, h_2, h_3$ are in $H.P.$Exradii are $r_1 = \frac{\Delta}{s-a}, r_2 = \frac{\Delta}{s-b}, r_3 = \frac{\Delta}{s-c}$. Since $a, b, c$ are in $A.P.$,$s-a, s-b, s-c$ are in $A.P.$ in reverse order,so their reciprocals are in $H.P.$Therefore,$r_1, r_2, r_3$ are in $H.P.$,not $A.P.$Thus,the statement in option $C$ is incorrect.

In $\Delta ABC$,if $a, b, c$ are in $A.P.$ (with usual notations),identify the incorrect statement -

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