Sequences And Series

Suppose $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $\mathrm{a}^2, 2 \mathrm{~b}^2, \mathrm{c}^2$ are in G.P. If $\mathrm{a}<\mathrm{b}<\mathrm{c}$ and $\mathrm{a}+\mathrm{b}+\mathrm{c}=1$, then $9\left(\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2\right)$ is equal to $\_\_\_\_$ .