# Math Help - Deductive geometry - Similarity and congruence

1. ## Deductive geometry - Similarity and congruence

Finally, the last geometry problem I am stuck with. Please help me get this one too!

Thanks so much to anyone who helps, I am certain this involves similarity and congruence.

2. We have $OE=2OD$.

But $OE=\frac{AC}{2}, \ OD=\frac{BC}{2}$.

Then $AC=2BC$.

Use Pitagora's theorem: $AC^2+BC^2=AB^2$.

Replace BC with $\frac{AC}{2}$ and AB with 10 and find AC.