# Geometry problem only needed hint one more

I just want hint how to use the congruent condition..which involves an equation in X I guess

And I obtained one equation $$y^2=x (16+x)$$

The condition $$AC\simeq BC$$ tells you that $$\angle ABF=\angle BCD$$. So, $$ABF$$ and $$DCF$$ are similar triangles. You get another equation from here.
Since $$\measuredangle BCD=\measuredangle CAB=\measuredangle B,$$ we obtain $$AB||CD$$ and from here we have the following system: $$y^2=x(x+16)$$ and $$\frac{y}{3}=\frac{x+10}{6}.$$ I got $$x=2.$$