I assume that if you extend the lines that intersect the $L$ edge you get isosceles triangles. Lets call the horizontal part of this $X$. Then you have similar triangles, where you can write $$\frac{X}{B}=\frac{X+C}{L}$$ You also have that $$X+C=\frac{A+X}{2}$$ These form a system with two linear equations with two unknowns, $X$ and $C$, which should be easy to solve.