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In the figure AB=4 , BC=6 , AC=5 and AD=6 what is length of DE ? Ans=9 enter image description here

I know there must be some property here that would solve this problem instantly but I cant figure it out any suggestions ? Edit: Since the two triangles are similar there corresponding sides will be equal in ratio , however I am still getting the wrong answer

BA   CA   BC 4    5    6 AE   6    DE 

$$AE = \frac{24}{5}$$ and $$DE = \frac{36}{5}$$

Where am I going wrong ?

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    You're applying the wrong similarity transform (a rotation instead of the reflection that's the actual similarity transform) and so getting the wrong cross ratios. You have AC:BC::AD:DE, (5:6::6:?) but in fact it's AB:BC::AD:DE (4:6::6:?).2012-07-17
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    One way to see why the symmetry should be reflection and not rotation is to consider moving A 'north' towards the top of the circle; then AC obviously shrinks, but on the other triangle the edge that shrinks is AE, not AD - so the similarity must be between ABC and ADE (note orientation), not ABC and AED.2012-07-17

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