\( \triangle A B C \) is right angled at \( C \) and \( D E \perp A...

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\( \triangle A B C \) is right angled at \( C \) and \( D E \perp A B \). Prove that \( \triangle A B C \sim \triangle A D E \) and hence find the lengths of \( A E \) and \( D E \).
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