Find A which is in a line

Question

Given lines c, a and b. a and b is vectical. How can I find A (which is in a) that AB equal to BC.

Answer 1

Extend the lines $a,b,c$ to the left until $a$ intersects $c$ (say, at $X$) and to the right until $b$ intersects $c$ (say at $Y$).

Then bisect $XY$ to get $B$ and construct a perpendicular to $c$ at $B$, extending it until both $a$ and $c$.