A geometry problem by Paola Ramírez

Let $\Delta ABC$ be an isosceles triangle with $AC=CB$ , $AB=7$ and height $CD = 9$ . Denote $a,b,c,d,e,f,g,h$ and $i$ to be parallel segments $AB$ and divide $CD$ into 9 equal segments.

Compute $a+b+c+d+e+f+g+h+i$ .