Explanation

(c)
$\frac{b}{c + a} - \frac{a}{b + c} = \frac{c}{a + b} - \frac{b}{c + a}\ \ \ \lbrack T_{2} - T_{1} = T_{3} - T_{2}\rbrack$
$\Rightarrow \ \frac{b^{2} + bc - ac - a^{2}}{(c + a)(b + c)} = \frac{c^{2} + ac - ab - b^{2}}{(a + b)(c + a)}$
$\Rightarrow \ \left\{ b^{2} - a^{2} - c(a - b) \right\}(a + b) = \left\{ c^{2} - b^{2} - a(b - c) \right\}(b + c)$
$\Rightarrow \ \left( b^{2} - a^{2} \right)(b + a + c) = \left( c^{2} - b^{2} \right)(a + b + c)$
$\Rightarrow \ 2b^{2} = a^{2} + c^{2}$
$\Rightarrow \ a^{2},b^{2},c^{2}$are in AP