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

http://i301.photobucket.com/albums/n.../Noether11.png

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

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- Sep 24th 2009, 05:15 AMBG5965Deductive geometry - Similarity and congruence
Finally, the last geometry problem I am stuck with. Please help me get this one too!

http://i301.photobucket.com/albums/n.../Noether11.png

Thanks so much to anyone who helps, I am certain this involves similarity and congruence. - Sep 24th 2009, 06:58 AMred_dog
We have $\displaystyle OE=2OD$.

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

Then $\displaystyle AC=2BC$.

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

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